CUET Mathematics - The shortest distance between the following lines: r = (i + j - k) + s(2i + j + k) r = (i + j + 2k) + t(4i + 2j + 2k), where s and t are scalars, is: | PYQs + Solutions

CUET Mathematics 2025 21 May Shift 2

Geometry

Medium

core

$\frac{3\sqrt{6}}{\sqrt{5}}$

$\sqrt{\frac{15}{2}}$

$\frac{\sqrt{5}}{3\sqrt{6}}$

$\sqrt{\frac{2}{15}}$

✅ Correct Option: 2

Related questions:

2 June Shift 1

If the direction ratios of two lines are $a, b, c$ and $(p-c), (c-a), (a-b)$ respectively, then the angle between these lines is:

27 May Shift 1

Let $L_1$ and $L_2$ be two lines, represented as,

$L_1: \vec{r} = \hat{i} + \hat{j} + \lambda(2\hat{i} - \hat{j} + \hat{k})$ and $L_2: \vec{r} = 2\hat{i} + \hat{j} - \hat{k} + \mu(4\hat{i} - 2\hat{j} + 2\hat{k})$ , where $\lambda$ and $\mu$ are scalars. Then which of the following are true?

(A) $L_1$ is perpendicular to $L_2$ .

(B) $L_1$ is parallel to $L_2$ .

(D) $L_2$ passes through the point (2, 1, -1)

Choose the correct answer from the options given below:

15 May Shift 1

Consider the lines $l_1: \frac{x-1}{0} = \frac{y-1}{1} = \frac{2-z}{1}$ and $l_2: \frac{x}{2} = \frac{y}{0} = \frac{2z-1}{-1}$ , then which of the following are correct?

(A) Direction Ratio's of $l_1 = <0, 1, 1>$

(B) Direction Ratio's of $l_2 = <2, 0, 2>$

(D) Angle between $l_1$ and $l_2$ is $\frac{2\pi}{3}$

Choose the correct answer from the options given below:

CUET Mathematics 2025 21 May Shift 2 PYQs

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