Assertion (A) : A line in space cannot be drawn perpendicular to x, y and z axes simultaneously. Reason (R) : For any line making angles, α, β, γ with the positive directions of x, y and z axes respectively, ²α + ²β + ²γ = 1. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.

MathsCBSE Class 12 · Board exam 2024, set 65/1/1 · 1 mark · Assertion-reason

CBSE Class 12 Mathematics 2024: question 20

Set in the CBSE Class 12 board exam of 2024, paper 65/1/1, section A, question 20, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q20 · 1 mark · Assertion-reasonCompetency-basedThree Dimensional Geometry

Assertion (A) : A line in space cannot be drawn perpendicular to x, y and z axes simultaneously.
Reason (R) : For any line making angles, $α, β, γ$ with the positive directions of x, y and z axes respectively, $cos^{2} α + cos^{2} β + cos^{2} γ = 1$ .

(A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(C)Assertion (A) is true, but Reason (R) is false.
(D)Assertion (A) is false, but Reason (R) is true.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 65/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

What would the angles be for a line perpendicular to all three axes?

Hint 2

Check those angles against the identity in R.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

If a line were perpendicular to all three axes, then $α = β = γ = 9 0^{\circ}$ , giving $cos^{2} α + cos^{2} β + cos^{2} γ = 0 \neq = 1$ .
½ mark
This contradicts R, which is a true identity, so A is true and R correctly explains it.
½ mark

Answer: (A)

Where the marks are

Uses the identity in R to show that A holds (1 mark)

Revise the chapter

Chapter: Three Dimensional Geometry (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Three Dimensional Geometry, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 65/1/1: every question, by section.

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CBSE Class 12 Mathematics 2024: question 20

Hints

Step-by-step solution

Revise the chapter

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