3D-PART-II-04-ASSIGNMENT

115. The perpndicular distance of the point (2, 4, –1) from the line is (a) 3 (b) 5 (c) 7 (d) 9 116. Distance of the point from the line , where l, m and n are the direction cosines of line is (a) (b) (c) (d) None of these 117. The length of the perpendicular from point (1, 2, 3) to the line is (a) 5 (b) 6 (c) 7 (d) 8 118. The foot of the perpendicular from (0, 2, 3) to the line is (a) (–2, 3, 4) (b) (2, –1, 3) (c) (2, 3, –1) (d) (3, 2, –1) 119. The foot of the perpendicular from (1, 2, 3) to the line joining the points (6, 7, 7) and (9, 9, 5) is (a) (5, 3, 9) (b) (3, 5, 9) (c) (3, 9, 5) (d) (3, 9, 9) 120. If the equation of a line through a point a and parallel to vector b is , where t is a parameter, then its perpendicular distance from the point c is (a) (b) (c) (d) 121. The distance of the point from the line which is passing through and which is parallel to the vector is (a) 10 (b) (c) (d) None of these 122. The ratio in which the line joining the points (a, b, c) and (–a, –c, –b) is divided by the xy-plane is (a) (b) (c) (d) 123. The ratio in which the line joining (2, 4, 5) (3, 5, –4) is divided by the yz-plane is (a) (b) (c) (d) 124. xy-plane divides the line joining the points (2, 4, 5) and (–4, 3, –2) in the ratio (a) (b) (c) (d) 125. The coordinates of the point where the line through P (3, 4, 1) and Q (5, 1, 6) crosses the xy-plane are (a) (b) (c) (d) 126. The plane XOZ divides the join of (1, –1, 5) and (2, 3, 4) in the ratio , then is (a) –3 (b) 3 (c) (d) 127. XOZ plane divides the join of (2, 3, 1) and (6, 7, 1) in the ratio (a) (b) (c) (d) 128. The plane meets the coordinate axes in A, B, C. The centroid of the triangle ABC is (a) (b) (c) (d) 129. The ratio in which the plane divides the line joining the points and is (a) (b) (c) (d) 130. If a plane cuts off intercepts , from the coordinate axes, then the area of the triangle ABC = (a) (b) (c) (d) 131. The plane cuts the axes in A, B, C, then the area of the is (a) (b) (c) (d) None of these 132. The volume of the tetrahedron included between the plane and the three coordinate planes is (a) (b) (c) 12 (d) None of these 133. A point located in space moves in such a way that sum of its distances from xy-and yz plane is equal to distance from zx plane, the locus of the point is (a) (b) (c) (d) 134. The equation of a plane parallel to x- axis is (a) (b) (c) (d) 135. In the space the equation represents a plane perpendicular to the plane (a) YOZ (b) Z=k (c) ZOX (d) XOY 136. The intercepts of the plane on the coordinate axes are (a) (10, 20, –10) (b) (10, –20, 12) (c) (12, –20, 10) (d) (12, 20, –10) 137. The coordinates of the points A and B are (2, 3, 4) and (–2, 5, –4) respectively. If a point P moves, so that where k is constant, then the locus of P is (a) A line (b) A plane (c) A sphere (d) None of these 138. In a three dimensional xyz space the equation represents (a) Points (b) Plane (c) Curves (d) Pair of straight line 139. The equation of yz-plane is (a) (b) (c) (d) 140. The intercepts of the plane on the coordinate axes are given by (a) 2, –3, 4 (b) 6, –4, –3 (c) 6, –4, 3 (d) 3, –2, 1.5 141. The locus of the point (x, y, z,) for which , is (a) A plane parallel to xy plane at a distance k from it (b) A plane parallel to yz plane at a distance k from it (c) A plane parallel to zx plane at a distance k from it (d) A line parallel to z-axis at a distance k from it 142. A point (x, y, z) moves parallel to x- axis. Which of the three variables x, y, z remains fixed (a) x (b) x and y (c) y and z (d) z and x 143. If a, b, c are three non-coplanar vectors, then the vector equation represents a (a) Straight line (b) Plane (c) Plane passing through the origin (d) Sphere 144. The direction cosines of the normal to the plane will be (a) 3, 4, 12 (b) (c) (d) 145. The direction cosines of the normal to the plane are (a) (b) (c) (d) 146. Normal form of the plane is (a) (b) (c) (d) None of these 147. The equation of a plane which cuts equal intercepts of unit length on the axes, is (a) (b) (c) (d) 148. The equation of the plane which is parallel to y- axis and cuts off intercepts of length 2 and 3 from x-axis and z¬¬-axis is (a) (b) (c) (d) 149. A planes  makes intercepts 3 and 4 respectively on z-axis and x-axis. If  is parallel to y- axis, then its equation is (a) (b) (c) (d) 150. The equation of the plane through the three points (1,1, 1), (1, –1, 1), and (–7, –3, –5), is (a) (b) (c) (d) None of these 151. The equation of the plane through (1, 2, 3) and parallel to the plane is (a) (b) (c) (d) 152. The equation of the plane through (2, 3, 4) and parallel to the plane is (a) (b) (c) (d) 153. The equation of the plane passing through the points (1, –3, –2) and perpendicular to planes and , is (a) (b) (c) (d) None of theses 154. The line drawn from (4, –1, 2) to the point (–3, 2, 3) meets a plane at right angles at the point (–10, 5, 4), then the equation of plane is (a) (b) (c) (d) None of these 155. together with represents in space (a) A line (b) A point (c) A plane (d) None of these 156. The equation of the plane which contains the line of intersection of the planes and and which is perpendicular to the plane , is (a) (b) (c) (d) 157. The equation of the planes passing through the line of intersection of the planes and , whose distance from the origin is 1, are (a) (b) (c) (d) None of these 158. The equation of the plane which passes through the point (2, 1, 4) and parallel to the plane is (a) (b) (c) (d) 159. The equation of a plane which passes through (2, –3, 1) and is normal to the line joining the points (3, 4, –1) and (2, –1, 5) is given by [AI CBSE 1990; MP PET 1993] (a) (b) (c) (d) 160. The coordinates of the point in which the line joining the points (3, 5, –7) and (–2, 1, 8) is intersected by the plane yz are given by (a) (b) (c) (d) 161. If P be the point (2, 6, 3), then the equation of the plane through P at right angle to OP, O being the origin, is (a) (b) (c) (d) 162. The equation of the plane containing the line of intersection of the planes and the perpendicular to the plane is (a) (b) (c) (d) 163. The equation of the plane passing through (1, 1, 1) and (1, –1, –1) and perpendicular to is (a) (b) (c) (d) 164. The equation of the plane through the intersection of the planes and and parallel to x-axis is (a) (b) (c) (d) 165. If O is the origin and A is the point (a, b, c), then the equation of the plane through A and at right angles to OA is (a) (b) (c) (d) None of these 166. The equation of the plane through the point (1, 2, 3) and parallel to the plane is (a) (b) (c) (d) None of these 167. The equation of the plane passing through the intersection of the planes and and the point (1, 1, 1), is [AISSE 1983] (a) (b) (c) (d) None of these 168. The equation of the plane passing through the intersection of the planes and and the origin is (a) (b) (c) (d) 169. If the plane is rotated through a right angle about its line of intersection with the plane , then the equation of plane in its new position is (a) (b) (c) (d) 170. The equation of the plane passing through the point (–2, –2, 2) and containing the line joining the points (1, 1, 1) and (1, –1, 2) is (a) (b) (c) (d) 171. The equation of the plane containing the line and passing through the point (2, 1, –1) is (a) (b) (c) (d) 172. In three dimensional space, the equation represents (a) A plane containing x-axis (b) A plane containing y-axis (c) A plane containing z-axis (d) A line with direction numbers 0, 3, 4 173. Direction ratios of the normal to the plane passing through the point (2, 1, 3) and the point of intersection of the planes and are (a) 13, 6, 1 (b) 5, 7, 3 (c) 4, 3, 2 (d) None of these 174. The plane of intersection of and is (a) (b) (c) (d) They do not intersect 175. If the planes and are at right angles, then the value of k is (a) (b) (c) (d) 2 176. The value of k for which the planes and are perpendicular to each other, is (a) 0 (b) 1 (c) 2 (d) 3 177. If the given planes and be mutually perpendicular, then (a) (b) (c) (d) 178. The angle between two planes is equal to (a) The angle between the tangents to them from any point (b) The angle between the normals to them from any point (c) The angle between the lines parallel to the planes from any point (d) None of these 179. If the planes and are mutually perpendicular, then (a) 3 (b) –3 (c) 9 (d) –6 180. The angle between the planes and is (a) 30° (b) 45° (c) 0° (d) 60° 181. The angle between the planes and is (a) (b) (c) (d) None of these 182. If is the angle between the planes , , then is equal to (a) (b) (c) (d) 183. The value of being negative, the origin will lie in the acute angle between the planes and if (a) (b) d and d' are of same sign (c) d and d' are of opposite sign (d) None of these 184. The equation of the plane which bisects the angle between the planes and which contains the origin is (a) (b) (c) (d) None of these 185. The equation of the bisector of the obtuse angle between the planes is (a) (b) (c) (d) 186. The two points (1, 1, 1) and (–3, 0, 1) with respect to the plane lie on (a) Opposite side (b) Same side (c) On the plane (d) None of these 187. Distance between parallel planes and is (a) (b) (c) (d) 2 188. The distance between the planes and is (a) (b) (c) (d) 189. Distance of the point (2, 3, 4) from the plane is (a) 1 (b) 2 (c) 3 (d) 0 190. The distance of the plane from the origin is (a) 2 (b) 1 (c) 14 (d) 8 191. The distance of the point (2, 3, –5) from the plane is (a) 4 (b) 3 (c) 2 (d) 1 192. If the points (1, 1, k) and (–3, 0, 1) be equidistant from the plane , then (a) 0 (b) 1 (c) 2 (d) None of these 193. If the product of distances of the point (1, 1, 1) from the origin and the plane be 5, then (a) –2 (b) –3 (c) 4 (d) 7 194. If two planes intersect, then the shortest distance between the planes is (a) (b) (c) (d) 1 195. The length of the perpendicular from the origin to the plane is (a) 3 (b) –4 (c) 5 (d) None of these 196. If the length of perpendicular drawn from origin on a plane is 7 units and its direction ratios are then that plane is (a) (b) (c) (d) 197. If a plane cuts off intercepts from the coordinate axes, then the length of the perpendicular from origin to the plane is (a) (b) (c) (d) 198. If and are points on a plane. A unit normal vector to the plane ABC is (a) (b) (c) (d) 199. If the position vectors of three points A, B and C are respectively and , then the unit vector to the plane containing the triangle ABC is (a) (b) (c) (d) None of these 200. The projection of point (a, b, c) in yz plane are (a) (0, b, c) (b) (a, 0, c) (c) (a, b, 0) (d) (a, 0, 0) 201. A variable plane at a constant distance p from origin meets the coordinate axes in A, B, C. Through these points planes are drawn parallel to coordinate planes. Then locus of the point of intersection is (a) (b) (c) (d) 202. A variable plane is at a constant distance p from the origin and meets the axes in A, B and C, then the locus of the centroid of the triangle ABC is (a) (b) (c) (d) None of these 203. The equation of the plane which bisects line joining (2, 3, 4) and (6, 7, 8) is (a) (b) (c) (d) 204. The equation of the plane which bisects the line joining the points (–1, 2, 3) and (3, –5, 6) at right angle, is (a) (b) (c) (d) 205. P is a fixed point (a, a, a) on a line through the origin equally inclined to the axes, then any plane through P perpendicular to OP, makes intercepts on the axes, the sum of whose reciprocals is equal to (a) a (b) (c) (d) None of these 206. If from a point P (a, b, c) perpendiculars PA and PB are drawn to yz and zx planes, then the equation of the plane OAB is (a) (b) (c) (d) 207. If and are the direction ratios of two intersecting lines, then the direction ratios of lines through them and coplanar with them are given by (a) (b) (c) (d) ,k being a number whatsoever 208. The four points (0, 4, 3), (–1, –5, –3), (–2, –2, 1) and (1, 1, –1) lie in the plane (a) (b) (c) (d) None of these 209. A plane meets the coordinate axes at A, B, C such that the centre of the triangle is (3, 3, 3). The equation of the plane is (a) (b) (c) (d) 210. Two system of rectangular axes have the same origin. If a plane cuts them at distance a, b,c and a', b', c' from the origin, then (a) (b) (c) (d) 211. Which one of the following is the best condition for the plane to intersect the x and y axes at equal angle (a) (b) (c) (d) 212. If the equation represents a pair of planes, then the angle between the pair of planes is (a) (b) (c) (d) 213. The points and determine a plane. The distance from the plane to the point is (a) (b) (c) (d) 214. The length and foot of the perpendicular from the point (7, 14, 5) to the plane , are (a) (b) (c) (d) 215. The distance of the point (1, 1, 1) from the plane passing through the points (2, 1, 1), (1, 2, 1) and (1, 1, 2) is (a) (b) 1 (c) (d) None of these 216. Perpendicular is drawn from the point (0, 3, 4) to the plane . The coordinates of the foot of the perpendicular are (a) (b) (c) (d) 217. The equation of the plane containing the lines and is (a) (b) (c) (d) 218. Let the points P, Q and R have position vectors ; and relative to an origin O. The distance of P from the plane OQR is (a) 2 (b) 3 (c) 1 (d) 5 219. The projection of the point (1, 3, 4) on the plane is (a) (1, 3, 4) (b) ( –3, 5, 2) (c) (–1, 4, 3) (d) None of these 220. If is the equation of plane and is a point, then a point equidistant from the plane on the opposite side is (a) (b) (c) (d) 221. If be the image of in the plane , then (a) (b) (c) Both (a) and (b) (d) None of these 222. The equation of the straight line passing through (1, 2, 3) and perpendicular to the plane is (a) (b) (c) (d) 223. The equation of the perpendicular from the point to the plane is (a) (b) (c) (d) None of these 224. The equation of the plane passing through the points and (1, 0, –1) and parallel to the line is (a) (b) (c) (d) None of these 225. The equation of the plane containing the line and the point (0, 7, –7) is (a) (b) (c) (d) None of these 226. The equation of plane through the line of intersection of planes and parallel to the line is (a) (b) (c) (d) None of these 227. The equation of the plane passing through the line and the point (4, 3, 7) is (a) (b) (c) (d) 228. The equation of the plane containing the line and parallel to the line is (a) (b) (c) (d) 229. The equation of the plane which is parallel to the line and passes through the points (0, 0, 0) and (3, –1, 2), is (a) (b) (c) (d) None of these 230. Equation of a line passing through (1, –2, 3) and parallel to the plane is (a) (b) (c) (d) None of these 231. The equation of the plane through the line and parallel to the line is (a) (b) (c) (d) None of these 232. The equation of the plane passing through the line and is (a) (b) (c) (d) None of these 233. The equation of the plane in which the lines and lie, is (a) (b) (c) (d) 234. The equation of the line passing through (1, 2, 3) and parallel to the planes and , is (a) (b) (c) (d) None of these 235. The plane and the line are related as (a) Parallel to the plane (b) Normal to the plane (c) Lies in the plane (d) None of these 236. The condition that the line lies in the plane is (a) and (b) and (c) and (d) and 237. and are the equation of line and plane respectively, then which of the following is true (a) The line is perpendicular to plane (b) The line lies in the plane (c) The line is parallel to plane but does not lie in plane (d) The line cuts the plane obliquely 238. The line joining the points (3, 5, –7) and (–2, 1, 8) meets the yz-plane at point (a) (b) (c) (d) (2, 2, 0) 239. Two lines which do not lie in the same plane are called (a) Parallel (b) Coincident (c) Intersecting (d) Skew 240. The planes pass through one line, if (a) (b) (c) (d) 241. The line lies in the plane . The values of k and d are (a) 4, 8 (b) –5, –3 (c) 5, 3 (d) –4, –8 242. If is the equation of the plane through the origin that contains the line , then (a) 1 (b) 3 (c) 5 (d) 7 243. If is the equation of the line through (1, 2, –1) and (–1, 0, 1); then (l, m, n) is (a) (–1, 0, 1) (b) (1, 1, –1) (c) (1, 2, –1) (d) (0, 1, 0) 244. Given the line and plane . Then of the following assertions, the only one that is always true is [DCE 1998; AMU 1991] (a) L is parallel to plane P (b) L is perpendicular to plane P (c) L lies in the plane P (d) None of these 245. The coordinates of the point where the line joining the points (2, –3, 1), (3, –4, –5) cuts the plane are (a) (2, 1, 0) (b) (3, 2, 5) (c) (1, –2, 7) (d) None of these 246. The point where the line meets the plane is (a) (3, –1, 1) (b) (3, 1, 1) (c) (1, 1, 3) (d) (1, 3, 1) 247. The coordinates of the point where the line meets the plane are (a) (2, 1, 0) (b) (7, –1, –7) (c) (1, 2, –6) (d) (5, –1, 1) 248. The point of intersection of the line and the plane is (a) (0, 1, –2) (b) (1, 2, 3) (c) (–1, 9, –25) (d) 249. If and be two non-parallel planes, then the equation represents the family of all planes through the line of intersection of the planes and , except the plane (a) (b) (c) (d) 250. The direction ratios of the normal to the plane passing through the points (1, –2, 3), (–1, 2, –1) and parallel to is (a) (2, 3, 4) (b) (4, 0, 7) (c) (–2, 0, –1) (d) (2, 0, –1) 251. The distance between the line and the plane is (a) 9 units (b) 1 unit (c) 2 units (d) 3 units 252. The distance of the point of intersection of the line and the plane from the point (3, 4, 5) is given by (a) 3 (b) (c) (d) None of these