CUET Mathematics - The vector equation of line passing through (2, -1, 3) and perpendicular to the lines x-2/3 = y-1/1 = z+2/2 and x+3/-4 = y-5/-3 = z+1/2 is (Here is a parameter) | PYQs + Solutions

CUET Mathematics 2025 29 May Shift 2

Geometry

Medium

core

$\vec{r} = (2\hat{i} - \hat{j} + 3\hat{k}) + \lambda(8\hat{i} - 14\hat{j} - 5\hat{k})$

$\vec{r} = (-2\hat{i} + \hat{j} - 3\hat{k}) + \lambda(8\hat{i} - 14\hat{j} - 5\hat{k})$

$\vec{r} = (-8\hat{i} - 14\hat{j} - 5\hat{k}) + \lambda(-2\hat{i} + \hat{j} + 3\hat{k})$

$\vec{r} = (8\hat{i} - 14\hat{j} - 5\hat{k}) + \lambda(2\hat{i} - \hat{j} + 3\hat{k})$

✅ Correct Option: 1

Related questions:

2 June Shift 1

The foot of the perpendicular drawn from the point $(1,6,3)$ to the line $\frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}$ is

22 May Shift 1

Match List-I with List-II

List-I	List-II
(A) Equations of line through $(5, -4, 6)$ with direction ratios $3, 7, 2$	(I) $\frac{x+3}{5} = \frac{y+7}{-4} = \frac{z+2}{6}$
(B) Equations of line through $(3, 7, 2)$ with direction ratios $5, -4, 6$	(II) $\frac{x-3}{5} = \frac{y-7}{-4} = \frac{z-2}{6}$
(C) Equations of line through $(-5, 4, -6)$ with direction ratios $3, 7, 2$	(III) $\frac{x-5}{3} = \frac{y+4}{7} = \frac{z-6}{2}$
(D) Equations of line through $(-3, -7, -2)$ with direction ratios $5, -4, 6$	(IV) $\frac{x+5}{3} = \frac{y-4}{7} = \frac{z+6}{2}$

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26 May Shift 2

Which of the following statements are true?

(A) The vector equation of the line through the point (5, 2, -4) and parallel to the vector $3\hat{i} + 2\hat{j} - 8\hat{k}$ is $\vec{r} = (5\hat{i} + 2\hat{j} - 4\hat{k}) + \lambda(3\hat{i} + 2\hat{j} - 8\hat{k})$

(B) Vector form of the equation of line $\frac{x-5}{3} = \frac{y+4}{7} = \frac{z-6}{2}$ is $\vec{r} = (5\hat{i} - 4\hat{j} + 6\hat{k}) + \lambda(3\hat{i} + 7\hat{j} + 2\hat{k})$

(D) If a line has direction ratios 2, -1, -2, then its direction cosines are -2/3, -1/3, -2/3.

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CUET Mathematics 2025 29 May Shift 2 PYQs

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