Assertion (A) : Equation of a line passing through the points (1, 2, 3) and (3, -1, 3) is (x-3)/(2) = (y+1)/(3) = (z-3)/(0). Reason (R) : Equation of a line passing through points (x_1, y_1, z_1), (x_2, y_2, z_2) is given by (x-x_1)/(x_2-x_1) = (y-y_1)/(y_2-y_1) = (z-z_1)/(z_2-z_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 and Reason (R) is false. (D) Assertion (A) is false and Reason (R) is true.

MathsCBSE Class 12 · Board exam 2023, set 65/1/1 · 1 mark · Assertion-reason

CBSE Class 12 Mathematics 2023: question 20

Set in the CBSE Class 12 board exam of 2023, 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) : Equation of a line passing through the points $(1, 2, 3)$ and $(3, - 1, 3)$ is $\frac{x - 3}{2} = \frac{y + 1}{3} = \frac{z - 3}{0}$ .
Reason (R) : Equation of a line passing through points $(x_{1}, y_{1}, z_{1})$ , $(x_{2}, y_{2}, z_{2})$ is given by $\frac{x - x _{1}}{x _{2} - x _{1}} = \frac{y - y _{1}}{y _{2} - y _{1}} = \frac{z - z _{1}}{z _{2} - z _{1}}$ .

(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 and Reason (R) is false.
(D)Assertion (A) is false and Reason (R) is true.

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

Hints

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

Hint 1

Compute $x_{2} - x_{1}, y_{2} - y_{1}, z_{2} - z_{1}$ .

Hint 2

Check the sign of the y-denominator.

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.

R is the standard two-point form: true.
½ mark
D.r.s are $2, - 3, 0$ , so the line is $\frac{x - 3}{2} = \frac{y + 1}{- 3} = \frac{z - 3}{0}$ ; given denominator 3 is wrong, A false. Option (D).
½ mark

Answer: Option (D)

Where the marks are

Finds d.r.s $2, - 3, 0$ so A false, R true (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 paper2023 board paper, set 65/1/1: every question, by section.

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CBSE Class 12 Mathematics 2023: question 20

Hints

Step-by-step solution

Revise the chapter

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