CUET Mathematics - Let L_1 and L_2 be two lines, represented as, L_1: r = i + j + (2i - j + k) and L_2: r = 2i + j - k + (4i - 2j + 2k), where and 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. (C) L_1 passes through the point (1, 1, 0) (D) L_2 passes through the point (2, 1, -1) Choose the correct answer from the options given below: | PYQs + Solutions

CUET Mathematics 2025 27 May Shift 1

Geometry

Medium

core

(A) and (D) only

(B), (C) and (D) only

(A) and (C) only

✅ Correct Option: 2

Related questions:

21 May Shift 1

The value of k for which the lines $\frac{2x - 3}{1} = \frac{3 - y}{k} = \frac{z - 2}{-2}$ and $\frac{x - 2}{1} = \frac{y}{4} = \frac{5 - z}{3}$ are perpendicular to each other 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:

16 May Shift 1

Consider the line $\frac{x-2}{2} = \frac{2y-5}{-3}, z = -1$ . Then which of the following is/are true?

(A) It has Direction ratios (2, -3, -1)

(B) It has Direction cosines $\left(\frac{4}{5}, \frac{-3}{5}, \frac{-1}{5}\right)$

(D) It has Direction cosines $\left(\frac{4}{5}, \frac{-3}{5}, 0\right)$

Choose the correct answer from the options given below:

CUET Mathematics 2025 27 May Shift 1 PYQs

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