The Cartesian equation of the line passing through the point (1,-3,2) and parallel to the line r=(2+λ)i++(2λ-1)k is (A) (x-1)/(2)=(y+3)/(0)=(z-2)/(-1) (B) (x+1)/(1)=(y-3)/(1)=(z+2)/(2) (C) (x+1)/(2)=(y-3)/(0)=(z+2)/(-1) (D) (x-1)/(1)=(y+3)/(1)=(z-2)/(2)

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

CBSE Class 12 Mathematics 2024: question 17

Set in the CBSE Class 12 board exam of 2024, paper 65/5/1, section A, question 17, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q17 · 1 mark · MCQThree Dimensional Geometry

The Cartesian equation of the line passing through the point $(1, - 3, 2)$ and parallel to the line $r = (2 + λ) \hat{i} + λ \hat{j} + (2 λ - 1) \hat{k}$ is

(A) $\frac{x - 1}{2} = \frac{y + 3}{0} = \frac{z - 2}{- 1}$
(B) $\frac{x + 1}{1} = \frac{y - 3}{1} = \frac{z + 2}{2}$
(C) $\frac{x + 1}{2} = \frac{y - 3}{0} = \frac{z + 2}{- 1}$
(D) $\frac{x - 1}{1} = \frac{y + 3}{1} = \frac{z - 2}{2}$

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

Separate the terms in $λ$ to read off the direction.

Hint 2

Parallel lines have the same direction ratios.

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 given line is $r = (2 \hat{i} - \hat{k}) + λ (\hat{i} + \hat{j} + 2 \hat{k})$ , so its direction ratios are $1, 1, 2$ .
½ mark
The required line through $(1, - 3, 2)$ is $\frac{x - 1}{1} = \frac{y + 3}{1} = \frac{z - 2}{2}$ , option (D).
½ mark

Answer: Option (D)

Where the marks are

Finds the direction ratios and writes the equation (1 mark)

Revise the chapter

Chapter: Three Dimensional Geometry (notes, formulas, where marks are lost and every past question)
Topic: Equation of a Line in Space

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.

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CBSE Class 12 Mathematics 2024: question 17

Hints

Step-by-step solution

Revise the chapter

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