Title 10.INTRODUCTION TO THREE DIMENSIONAL GEOMETRY.pdf ✅

10. INTERODUCTION TO THREE DIMENSIOANL (1.) Let the line 2 1 2 3 5 2 x y z − − + = = − lie in the plane x y z + − + = 3 0   . Then ( , ) equals [AIEEE-2009] (a.) (−6,7) (b.) (5, 15 − ) (c.) (−5,5) (d.) (6, 17 − ) (2.) A line AB in three-dimensional space makes angles 45 and 120 with the positive x -axis and the positive y -axis respectively. If AB makes an acute angle  with the positive z -axis, then  equals [AIEEE-2010] (a.) 30 (b.) 45 (c.) 60 (d.) 75 (3.) Statement-1 : The point A(3,1,6) is the mirror image of the point B(1,3, 4) in the plane x y − + z = 5. Statement-2: The plane x y z − + = 5 bisects the line segment joining A(3,1,6) and B(1,3, 4). [AIEEE-2010] (a.) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1 (b.) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1 (c.) Statement-1 is true, Statement- 2 is false (d.) Statement-1 is false, Statement- 2 istrue (4.) There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points, then [AIEEE-2011] (a.) 140 190   N (b.) N 190 (c.) N 100 (d.) 100 140   N (5.) The length of the perpendicular drawn from the point (3, 1,11 − ) to the line 2 3 2 3 4 x y z − − = = is [AIEEE-2011] (a.) 53 (b.) 66 (c.) 29 (d.) 33 (6.) The distance of the point (1, 5,9 − ) from the plane x y z − + = 5 measured along a straight line x y z = = is [AIEEE-2011] (a.) 3 10 (b.) 3 5 (c.) 10 3 (d.) 5 3 (7.) An equation of a plane parallel to the plane x y z − + − = 2 2 5 0 and at a unit distance from the origin is [AIEEE-2012] (a.) x y z − + + = 2 2 1 0 (b.) x y z − + − = 2 2 1 0 (c.) x y z − + + = 2 2 5 0 (d.) x y z − + − = 2 2 3 0
(8.) If the lines 1 1 1 2 3 4 x y z − + − = = and 3 1 2 1 x y k z − − = = intersect, then k is equal to [AIEEE-2012] (a.) 2 9 (b.) 9 2 (c.) 0 (d.) -1 (9.) Distance between two parallel planes 2 2 8 x y z + + = and 4 2 4 5 0 x y z + + + = is [JEE (Main)-2013] (a.) 3 2 (b.) 5 2 (c.) 7 2 (d.) 9 2 (10.) If the lines 2 3 4 1 1 x y z k − − − = = − and 1 4 5 2 1 x y z k − − − = = are coplanar, then k can have [JEE (Main)-2013] (a.) Any value (b.) Exactly one value (c.) Exactly two values (d.) Exactly three values (11.) The image of the line 1 3 4 3 1 5 x y z − − − = = − in the plane 2 3 0 x y z − + + = is the line [JEE (Main)-2014] (a.) 3 5 2 3 1 5 xyz − + − = = − (b.) 3 5 2 3 1 5 xyz − + − = = − − (c.) 3 5 2 3 1 5 x y z + − − = = − (d.) 3 5 2 3 1 5 x y z + − + = = − − (12.) The distance of the point (1,0, 2) from the point of intersection of the line 2 1 2 3 4 12 x y z − + − = = and the plane x y z − + =16 , is [JEE (Main)-2015] (a.) 2 14 (b.) 8 (c.) 3 21 (d.) 13 (13.) The equation of the plane containing the line 2 5 3; 4 5 x y z x y z − + = + + = , and parallel to the plane, x y z + + = 3 6 1 , is [JEE (Main)-2015] (a.) 2 6 12 13 x y z + + = (b.) x y z + + = − 3 6 7 (c.) x y z + + = 3 6 7 (d.) 2 6 12 13 x y z + + = − (14.) If the line, 3 2 4 2 1 3 x y z − + + = = − lies in the plane, lx my z + − = 9 , then 2 2 I m+ is equal to [JEE (Main)-2016] (a.) 18 (b.) 5 (c.) 2 (d.) 26 (15.) The distance of the point (1, 5,9 − ) from the plane x y z − + = 5 measured along the line x y z = = is [JEE (Main)-2016]
(a.) 10 3 (b.) 10 3 (c.) 20 3 (d.) 3 10 (16.) The distance of the point (1,3, 7− ) from the plane passing through the point (1, 1, 1 − − ) , having normal perpendicular to both the lines 1 2 4 1 2 3 x y z − + − = = − and 2 1 7 2 1 1 x y z − + + = = − − , is [JEE (Main)-2017] (a.) 10 83 (b.) 5 83 (c.) 10 74 (d.) 20 74 (17.) If the image of the point P(1, 2,3 − ) in the plane, 2 3 4 22 0 x y z + − + = measured parallel to the line, 1 4 5 x y z = = is Q , then PQ is equal to [JEE (Main)-2017] (a.) 2 42 (b.) 42 (c.) 6 5 (d.) 3 5 (18.) If L1 is the line of intersection of the planes 2 2 3 2 0, 1 0 x y z x y z − + − = − + + = and L2 is the line of intersection of the planes x y z x y z + − − = − + − = 2 3 0,3 2 1 0 , then the distance of the origin from the plane containing the lines L1 and L2 , is [JEE (Main)-2018] (a.) 1 4 2 (b.) 1 3 2 (c.) 1 2 2 (d.) 1 2 (19.) The length of the projection of the line segment joining the points (5, 1, 4 − ) and (4, 1,3 − ) on the plane, x y z + + = 7 is: [JEE (Main)-2018] (a.) 2 3 (b.) 2 3 (c.) 1 3 (d.) 2 3 (20.) The plane through the intersection of the planes x y z + + =1 and 2 3 4 0 x y z + − + = and parallel to y -axis also passes through the point [JEE (Main)-2019] (a.) (3, 2,1) (b.) (3,3, 1− ) (c.) (− − 3,0, 1) (d.) (−3,1,1) (21.) The equation of the line passing through (−4,3,1) , parallel to the plane x y z + − − = 2 5 0 and intersecting the line 1 3 2 3 2 1 x y z + − − = = − − is [JEE (Main)- 2019] (a.) 4 3 1 2 2 4 x y z − + + = = (b.) 4 3 1 1 1 1 x y z + − − = = − (c.) 4 3 1 3 1 1 x y z + − − = = − (d.) 4 3 1 1 1 3 x y z + − − = =
(22.) If the lines x ay b z cy d = + = + , and x a z =  + b y c z d   , = +  are perpendicular, then [JEE (Main)-2019] (a.) ab bc + + 1 0 = (b.) cc a a   + + = 0 (c.) aa c c   + + = 0 (d.) bb cc + + 1 0 = (23.) The equation of the plane containing the straight line 2 3 4 x y z = = and perpendicular to the plane containing the straight lines 3 4 2 x y z = = and 4 2 3 x y z = = is [JEE (Main)- 2019] (a.) x y z − + = 2 0 (b.) x y z + − = 2 2 0 (c.) 5 2 4 0 x y z + − = (d.) 3 2 3 0 x y z + − = (24.) The plane passing through the point (4, 1, 2 − ) and parallel to the lines 2 2 1 3 1 2 x y z + − + = = − and 2 3 4 1 2 3 x y z − − − = = also passes through the point [JEE (Main)-2019] (a.) (−−− 1, 1, 1) (b.) (− − 1, 1,1) (c.) (1,1,1) (d.) (1,1, 1− ) (25.) Let A be a point on the line ( ) ( ) ( ) ˆ ˆ ˆ r i j k = − + − + + 1 3 1 2 5    and B(3,2,6) be a point in the space. Then the value of  for which the vector AB is parallel to the plane x y z − + = 4 3 1 is [JEE (Main)-2019] (a.) 1 4 (b.) 1 2 (c.) 1 8 (d.) 1 4 − (26.) The plane which bisects the line segment joining the points (− − 3, 3, 4) and (3,7,6) at right angles, passes through which one of the following points? [JEE (Main)-2019] (a.) (−2,3,5) (b.) (4,1, 2− ) (c.) (2,1,3) (d.) (4, 1,7 − ) (27.) On which of the following lines lies the point of intersection of the line, 4 5 3 2 2 1 x y z − − − = = and the plane, x y z + + = 2 ? [JEE (Main)-2019] (a.) 134 1 2 5 x y z − − + = = − (b.) 3 4 1 3 3 2 x y z + − + = = − (c.) 4 5 5 1 1 1 x y z − − − = = − (d.) 2 3 3 2 2 3 x y z − − + = = (28.) The plane containing the line 3 2 1 2 1 3 x y z − + − = = − and also containing its projection on the plane 2 3 5 x y z + − = , contains which one of the following points? [JEE (Main)-2019] (a.) (0, 2, 2 − ) (b.) (2, 2,0) (c.) (−2, 2, 2) (d.) (2,0, 2− )