CUET Mathematics - The shortest distance between the lines r = i + j + (2i - j + k) and r' = 2i + j - k + (4i - 2j + 2k) is | PYQs + Solutions

CUET Mathematics 2025 3 June Shift 1

Geometry

Medium

core

$\frac{\sqrt{66}}{6}$

$6\sqrt{66}$

$\sqrt{66}$

✅ Correct Option: 1

Related questions:

3 June Shift 2

The vector equation of line passing through $(-1, -1, -2)$ and perpendicular to the lines $\frac{x+4}{1} = \frac{y}{-2} = \frac{z-3}{3}$ and $\frac{x+2}{-3} = \frac{y+5}{2} = \frac{z-6}{5}$ is

29 May Shift 2

Let the equation of lines be as $L_1: \vec{r} = \vec{a_1} + \lambda\vec{b_1}$ and $L_2: \vec{r} = \vec{a_2} + \lambda\vec{b_2}$ such that $\vec{d_1} - \vec{d_2} = 2\hat{i} + 4\hat{j} + 4\hat{k}$ 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

13 May Shift 1

Consider two lines $l_1$ and $l_2$ with cartesian equations $\frac{x}{2} = \frac{1-y}{-2} = \frac{z}{1}$ and $\frac{2x-5}{16} = \frac{y-2}{-1} = \frac{z-5}{4}$ respectively. Which of the following is/are true?

(A) Direction ratio of $l_1$ are 2, 2, 1

(B) Direction cosines of $l_1$ are $\frac{2}{3}, \frac{-2}{3}, \frac{1}{3}$

(D) Angle between $l_1$ and $l_2$ is $\cos^{-1}\left(\frac{38}{3\sqrt{273}}\right)$

Choose the correct answer from the options given below:

CUET Mathematics 2025 3 June Shift 1 PYQs

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