MCQ Questions Class 12 Three Dimensional Geometry With Answers

CBSE Class 12 Three Dimensional Geometry Multiple Choice Questions with Answers. MCQ Questions Class 12 Three Dimensional Geometry with Answers Is Prepared Based on Latest Exam Pattern. Students can solve NCERT MCQ questions Class 12 Three Dimensional Geometry with Answers to know their preparation level.

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MCQ Questions Class 12 Three Dimensional Geometry with Answers - Set - 3

Question 1:

What are the direction cosines of the equation of the plane 2x + 3y – z = 5?

A. 1/√14, 3/√14, -2/√14

B. 2/√14, 3/√14, -1/√14

C. 2/√14, 1/√14, -1/√14

D. 2/√14, -2/√14, -3/√14

Check Answer

Correct Answer – (B)

The equation of the plane, 2x + 3y – z = 5…. (1)

Direction ratio of the normal (2, 3, -1)

By using the formula,

√[(2)2 + (3)2 + (-1)2] = √14

Now,

Divide both the sides of equation (1) by √14, we get

2x/(√14) + 3y/(√14) – z/(√14) = 5/√14

So this is of the form lx + my + nz = d

Where, l, m, n are the direction cosines and d is the distance

Therefore, the direction cosines are 2/√14, 3/√14, -1/√14

Question 2:

The vector equation for the line passing through the points (–1, 0, 2) and (3, 4, 6) is:

A. i + 2k + λ(4i + 4j + 4k)

B. i – 2k + λ(4i + 4j + 4k)

C. -i+2k+ λ(4i + 4j + 4k)

D. -i+2k+ λ(4i – 4j – 4k)

Check Answer

Correct Answer – (C)

The vector equation of the line is given by:

r = a + λ (b – a), λ ∈ R

Let a = -i + 2k

And b = 3i + 4j + 6k

b – a = 4i + 4j + 4k

Let the vector equation be r, then;

r = -i + 2k + λ (4i + 4j + 4k)

Question 3:

Direction ratio of line joining (2, 3, 4) and (−1, −2, 1), are:

A. (−3, −5, −3)

B. (−3, 1, −3)

C. (−1, −5, −3)

D. (−3, −5, 5)

Check Answer

Correct Answer – (A)

The direction ratio of the line joining A (2, 3, 4) and B (−1, −2, 1), are:

(−1−2), (−2−3), (1−4)

= (−3, −5, −3)

Question 4:

The direction ratios of the normal to the plane 7x + 4y – 2z + 5 = 0 are:

A. 7, 4,-2

B. 7, 4, 5

C. 7, 4, 2

D. 4, -2, 5

Check Answer

Correct Answer – (A)

Question 5:

Find the equation of the plane passing through the points P(1, 1, 1), Q(3, -1, 2), R(-3, 5, -4).

A. x + 2y = 0

B. x – y – 2 = 0

C. -x + 2y – 2 = 0

D. x + y – 2 = 0

Check Answer

Correct Answer – (D)

MCQ Questions Class 12 Three Dimensional Geometry With Answers

Question 6:

If the lines x-2/1 =y-2/1 =z-4/k and x-1/k = y-4/2 = z-5/1 are coplanar, then k can have:

A. Exactly two values

B. Exactly three values

C. Exactly one value

D. Any value

Check Answer

Correct Answer – (A)

Question 7:

If a line has direction ratios 2, – 1, – 2, determine its direction cosines:

A. ⅓, ⅔, -⅓

B. ⅔, -⅓, -⅔

C. -⅔, ⅓, ⅔

D. None of the above

Check Answer

Correct Answer – (B)

Explanation: Direction cosines are:

= $\frac{2}{\sqrt{2^{2} + (- 1)^{2} + (- 2)^{2}}}, \frac{- 1}{\sqrt{2^{2} + (- 1)^{2} + (- 2)^{2}}}, \frac{- 2}{\sqrt{2^{2} + (- 1)^{2} + (- 2)^{2}}}$

= ⅔, -⅓, -⅔

Question 8:

If l, m, n are the direction cosines of a line, then;

A. l²+ m²+ 2n² = 1

B. l²+ 2m²+ n² = 1

C. 2l²+ m²+ n² = 1

D. l²+ m²+ n² = 1

Check Answer

Correct Answer – (D)

Question 9:

The equation x² – x – 2 = 0 in three-dimensional space is represented by:

A. A pair of parallel planes

B. A pair of straight lines

C. A pair of the perpendicular plane

D. None of these

Check Answer

Correct Answer – (A)

Question 10:

The direction cosines of the y-axis are:

A. (9, 0, 0)

B. (1, 0, 0)

C. (0, 1, 0)

D. (0, 0, 1)

Check Answer

Correct Answer – (C)

MCQ Questions Class 12 Three Dimensional Geometry With Answers

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MCQ Questions Class 12 Three Dimensional Geometry With Answers

MCQ Questions Class 12 Three Dimensional Geometry with Answers - Set - 3

Correct Answer – (B)

Correct Answer – (C)

Correct Answer – (A)

Correct Answer – (A)

Correct Answer – (D)

MCQ Questions Class 12 Three Dimensional Geometry With Answers

Correct Answer – (A)

Correct Answer – (B)

Correct Answer – (D)

Correct Answer – (A)

Correct Answer – (C)

MCQ Questions Class 12 Three Dimensional Geometry With Answers

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MCQ Questions Class 12 Three Dimensional Geometry With Answers

MCQ Questions Class 12 Three Dimensional Geometry with Answers - Set - 3

Correct Answer – (B)

Correct Answer – (C)

Correct Answer – (A)

Correct Answer – (A)

Correct Answer – (D)

MCQ Questions Class 12 Three Dimensional Geometry With Answers

Correct Answer – (A)

Correct Answer – (B)

Correct Answer – (D)

Correct Answer – (A)

Correct Answer – (C)

MCQ Questions Class 12 Three Dimensional Geometry With Answers

MCQ Questions Class 12 Vector Algebra With Answers

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