The angle which the line x/1=(y)/(-1)=z/0 makes with the positive direction of Y-axis is : (A) (5π)/(6) (B) (3π)/(4) (C) (5π)/(4) (D) (7π)/(4)

MathsCBSE Class 12 · Board exam 2024, set 65/5/1 · 1 mark · MCQ

CBSE Class 12 Mathematics 2024: question 16

Set in the CBSE Class 12 board exam of 2024, paper 65/5/1, section A, question 16, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q16 · 1 mark · MCQThree Dimensional Geometry

The angle which the line $\frac{x}{1} = \frac{y}{- 1} = \frac{z}{0}$ makes with the positive direction of Y-axis is :

(A) $\frac{5 π}{6}$
(B) $\frac{3 π}{4}$
(C) $\frac{5 π}{4}$
(D) $\frac{7 π}{4}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 65/5/1.

Hints

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

Hint 1

Convert the direction ratios into direction cosines.

Hint 2

The angle must lie in $[0, π]$ .

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.

The direction ratios are $1, - 1, 0$ , so the direction cosines are $\frac{1}{2}, - \frac{1}{2}, 0$ .
½ mark
$cos β = - \frac{1}{2}$ , so $β = \frac{3 π}{4}$ , option (B).
½ mark

Answer: $\frac{3 π}{4}$ , option (B)

Where the marks are

Finds $cos β$ from the direction cosines (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 65/5/1: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 12 Mathematics 2024: question 16

Hints

Step-by-step solution

Revise the chapter

More questions from Three Dimensional Geometry