CUET Mathematics - The vector equation of line passing through (-1, -1, -2) and perpendicular to the lines x+4/1 = y/-2 = z-3/3 and x+2/-3 = y+5/2 = z-6/5 is | PYQs + Solutions

CUET Mathematics 2025 3 June Shift 2

Geometry

Medium

core

$\vec{r} = (-3\hat{i} + 4\hat{j} + 15\hat{k}) + \lambda(-1 + 3\hat{j} - 2\hat{k})$

$\vec{r} = (-1 + 3\hat{j} - 2\hat{k}) + \lambda(-3\hat{i} + \hat{j} + 15\hat{k})$

$\vec{r} = 2\hat{i} - 7\hat{j} + \hat{k} + \lambda(-1 + \hat{j} - 2\hat{k})$

$\vec{r} = (-1 + \hat{j} - 2\hat{k}) + \lambda(2\hat{i} - 7\hat{j} + \hat{k})$

✅ Correct Option: 4

Related questions:

22 May Shift 1

If the lines $\frac{1-x}{3} = \frac{y-2}{2\lambda} = \frac{z-3}{2}$ and $\frac{x-1}{3\lambda} = \frac{y-1}{1} = \frac{6-z}{5}$ are perpendicular, then $\lambda$ is equal to

22 May Shift 2

Match List-I with List-II

List-I	List-II
Equation of line	Information
(A) $\vec{r} = (3\hat{i} - 2\hat{j} + \hat{k}) + \lambda(\hat{j} - 2\hat{k})$	(I) Direction ratios are 2, 4, -1
(B) $\frac{2-x}{1} = \frac{2y+1}{4}$ , $z = 2$	(II) Perpendicular to $2\hat{i} - \hat{j} + \hat{k}$
(C) $\frac{x}{1} = \frac{y-3}{2} = \frac{3-4z}{2}$	(III) Passing through the point $(3, -2, 1)$
(D) $\vec{r} = (3\hat{i} + 2\hat{j} + \hat{k}) + \lambda(2\hat{i} + \hat{j} - 3\hat{k})$	(IV) Direction ratios are -1, 2, 0

Choose the correct answer from the options given below:

21 May Shift 1

If a line makes angles $\alpha$ , $\beta$ and $\gamma$ with the positive directions of coordinate axes respectively, then $\cos 2\alpha + \cos 2\beta + \cos 2\gamma$ is equal to

CUET Mathematics 2025 3 June Shift 2 PYQs

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