The angle between the lines 2x = 3y = -z and 6x = -y = -4z is (A) 0° (B) 30° (C) 45° (D) 90°

MathsCBSE Class 12 · Board exam 2023, set 65/5/1 · 1 mark · MCQ

CBSE Class 12 Mathematics 2023: question 16

Set in the CBSE Class 12 board exam of 2023, 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 between the lines $2 x = 3 y = - z$ and $6 x = - y = - 4 z$ is

(A) $0^{\circ}$
(B) $3 0^{\circ}$
(C) $4 5^{\circ}$
(D) $9 0^{\circ}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 65/5/1.

Hints

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

Hint 1

Write each line in symmetric form to read direction ratios.

Hint 2

Compute $a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2}$ .

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.

Line 1: $\frac{x}{1/2} = \frac{y}{1/3} = \frac{z}{- 1}$ , dr's $3, 2, - 6$ . Line 2: $\frac{x}{1/6} = \frac{y}{- 1} = \frac{z}{- 1/4}$ , dr's $2, - 12, - 3$ .
$3 (2) + 2 (- 12) + (- 6) (- 3) = 6 - 24 + 18 = 0$ , so lines are perpendicular: $9 0^{\circ}$ .
1 mark

Answer: $9 0^{\circ}$ , option (D)

Where the marks are

Direction ratios and zero dot product (1 mark)

Revise the chapter

Chapter: Three Dimensional Geometry (notes, formulas, where marks are lost and every past question)
Topic: Shortest Distance Between Two Lines

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 paper2023 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 2023: question 16

Hints

Step-by-step solution

Revise the chapter

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