NCERT MCQ CLASS-12 CHAPTER-11 | MATH NCERT MCQ | THREE DIMENSIONAL GEOMETRY | EDUGROWN

In This Post we are  providing Chapter-11 Three Dimensional Geometry NCERT MCQ for Class 12 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON THREE DIMENSIONAL GEOMETRY

Question 1.
Distance between two planes:
2x + 3y + 4z = 5 and 4x + 6y + 8z = 12 is
(a) 2 units
(b) 4 units
(c) 8 units
(d) 129√ units.

Answer: (d) 129√ units.

Question 2.
The planes 2x – y + 4z = 3 and 5x – 2.5y +10 z = 6 are
(a) perpendicular
(b) parallel
(c) intersect along y-axis
(d) passes through (0, 0, 54)

Answer: (b) parallel

Question 3.
The co-ordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are given by:
(a) (2, 0, 0)
(b) (0, 5, 0)
(c) (0, 0, 7)
(d) (0, 5, 7).

Answer: (a) (2, 0, 0)

Question 4.
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:
(a) < sin α, sin ß, sin γ >
(b) < cos α, cos ß, cos γ >
(c) < tan α, tan ß, tan γ >
(d) < cos² α, cos² ß, cos² γ >

Answer: (b) < cos α, cos ß, cos γ >

Question 5.
The distance of a point P(a, b, c) from x-axis is
(a)  √ a2+c2
(b)  √ a2+b2
(c)  √ b2+c2
(d) b² + c².

Answer: (c) √  b2+c2

Question 6.
If the direction-cosines of a line are < k, k, k >, then
(a) k > 0
(b) 0 < k < 1
(c) k = 1
(d) k = 1√3 or –1√3

Answer: (c) k = 1

Question 7.
The reflection of the point (α, ß, γ) in the xy-plane is:
(a) (α, ß, 0)
(b) (0, 0, γ)
(c) (-α, -ß, γ)
(d) (α, ß, -γ).

Answer: (d) (α, ß, -γ).

Question 8.
What is the distance (in units) between two planes:
3x + 5y + 7z = 3 and 9x + 15y + 21z = 9?
(a) 0
(b) 3
(c) 68√3
(d) 6

Answer: (a) 0

Question 9.
The equation of the line in vector form passing through the point (-1, 3, 5) and parallel to line x−32 = y−43, z = 2 is
(a) r⃗  = (-i^ + 3j^ + 5k^) + λ(2i^ +3j^ + k^)
(b) r⃗  = (-i^+ 3j^ + 5k^) + λ(2i^ + 3j^)
(c) r⃗  = (2i^+ 3j^ – 2k^) + λ(-i^ + 3j^ + 5k^)
(d) r⃗  = (2i^ + 3j^]) + λ(-i^ + 3j^ + 5k^).

Answer: (b) r⃗  = (-i^+ 3j^ + 5k^) + λ(2i^ + 3j^)

Question 10.
Let the line x−23 = y−1−5 = z−22 lie in the plane x + 3y – αz + ß = 0. Then (α, ß) equals:
(a) (-6, -17)
(b) (5, -15)
(c) (-5, 5)
(d) (6, -17).

Answer: (a) (-6, -17)

Question 11.
The projections of a vector on the three co-ordinate axes are 6, -3, 2 respectively. The direction-cosines of the vector are:
(a) 65, –35, 25
(b) 67, –37, 27
(c) −67, −37, 17
(d) 6, -3, 2.

Answer: (b) 67, –37, 27

Question 12.
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:
(a) 30°
(b) 45°
(c) 60°
(d) 15°.

Answer: (c) 60°

Question 13.
If the angle between the line x = y−12 = z−3λ and the plane x + 2y + 3z = 4is cos^-1 (√514) then λ, equals:
(a) 23
(b) 32
(c) 25
(d) 53

Answer: (a) 23

Question 14.
The length of the perpendicular drawn from the point (3, -1, 11) to the line x2 = y−23 = z−34 is
(a) √29
(b) √33
(c) √53
(d) √65

Answer: (c) √53

Question 15.
The distance of the point (1, -5, 9) from the plane x – y + z = 5, measured along a straight line x = y = z is:
(a) 10√3
(b) 5√3
(c) 10 √3
(d) 3√5

Answer: (a) 10√3

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