If two lines x-3/2 = y-4/5 = z/4 and x-4/3 = y-5/6 = 1-z/k, are coplanar, then k is equal to Option 1: 5 Option 2: -5 Option 3: 9 Option 4: -3

The answer is '-5'. View full solution:

CUET Mathematics - If two lines x-3/2 = y-4/5 = z/4 and x-4/3 = y-5/6 = 1-z/k, are coplanar, then k is equal to | PYQs + Solutions

CUET Mathematics 2022 6 Aug Shift 2

Geometry

Hard

$5$

$-5$

$9$

$-3$

✅ Correct Option: 2

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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:

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Let the equation of lines be as $L_1: \vec{r_1} = \vec{a_1} + \lambda\vec{b_1}$ and $L_2: \vec{r_2} = \vec{a_2} + \lambda\vec{b_2}$ such that $\vec{a_1} - \vec{a_2} = 2\hat{i} + 4\hat{j} + 4\hat{k}$ and $\vec{b_1} \times \vec{b_2} = 8\hat{i} - 4\hat{k}$ . Then the shortest distance between $L_1$ and $L_2$ is

CUET Mathematics 2022 6 Aug Shift 2 PYQs

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