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Class 12 Mathematics - Chapter 11: Three Dimensional Geometry MCQ Questions

22 Questions 44 Minutes
Answered: 0 / 22Unanswered: 22

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Question 1

2x – y + z + 3 = 0 is the line:

Question 2

The planes 2x – y + 4z = 3 and 5x – 2.5y +10 z = 6 are

Question 3

If the angle between the line x = (frac { y-1 }{2}) = (frac { z-3 }{λ}) and the plane x + 2y + 3z = 4is cos-1 ((sqrt{frac { 5}{14}})) then λ, equals:

Question 4

The equation of the plane containing the line: 2x – 5y + z = 3; x + y + 4z = 5 and parallel to the plane: x + 3y + 6z = 1 is:

Question 5

An equation of a plane parallel to the plane x – 2y + 2z – 5 = 0 and at a unit distance from the origin is:

Question 6

The length of the perpendicular drawn from the point (3, -1, 11) to the line (frac { x }{2}) = (frac { y-2 }{3}) = (frac { z-3 }{4}) is

Question 7

(frac { x-2 }{3}) = (frac { y+1 }{4}) = (frac { z-2 }{12}) and flie plane x – y + z = 16 is

Question 8

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 θ with the positive z-axis, then θ equals:

Question 9

2x + 3y + 4z = 5 and 4x + 6y + 8z = 12 is

Question 10

If the lines: (frac { x-2 }{1}) = (frac { y-3 }{1}) = (frac { z-4 }{-k}) and (frac { x-1 }{k}) = (frac { y-4 }{2}) = (frac { z-5 }{1}) are coplanar, then k can have:

Question 11

2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

Question 12

The projections of a vector on the three co-ordinate axes are 6, -3, 2 respectively. The direction-cosines of the vector are:

Question 13

The distance of a point P(a, b, c) from x-axis is

Question 14

The reflection of the point (α, ß, γ) in the xy-plane is:

Question 15

3x + 5y + 7z = 3 and 9x + 15y + 21z = 9?

Question 16

If α, ß, γ are the angles that a line makes with the positive direction of x, y, z axis, respectively, then the direction-cosines of the line are:

Question 17

The co-ordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are given by:

Question 18

The equation of the line in vector form passing through the point (-1, 3, 5) and parallel to line (frac { x-3 }{2}) = (frac { y-4 }{3}), z = 2 is

Question 19

Let the line (frac { x-2 }{3}) = (frac { y-1 }{-5}) = (frac { z-2 }{2}) lie in the plane x + 3y – αz + ß = 0. Then (α, ß) equals:

Question 20

If the direction-cosines of a line are < k, k, k >, then

Question 21

The distance of the point (1, -5, 9) from the plane x – y + z = 5, measured along a straight line x = y = z is:

Question 22

If the line (frac { x-3 }{2}) = (frac { y+2 }{-1}) = (frac { z+4 }{3}) lies in the plane lx + my – z = 9,then l² + m² is equal to

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