CUET Mathematics - Direction cosines of 2 lines are given by the equations 3l+m+5n=0, 6mn-2nl+5lm=0 then which of the following statements are correct ? (A) Direction ratios of two lines are (1, 2, -1) and (-2, 1, 1). (B) Angle between lines is /3. (C) The angle between the lines is ^-1(-1/6). (D) Vectors parallel to these lines are i+2 j- k and -2 i+ j+ k. Choose the correct answer from the options given below: | PYQs + Solutions

CUET Mathematics 2026 22nd May Shift 1

Geometry

Hard

core

(A), (B) and (C) only

(A) and (C) only

(A), (C) and (D) only

✅ Correct Option: 4

Related questions:

21st May Shift 2

Match the LIST-I with LIST-II

LIST-I (Line)		LIST-II (Direction cosiness)
A. $\vec{r} = (2\hat{i} - \hat{j} + \hat{k}) + \lambda(3\hat{i} + 2\hat{k})$		I. $\left\langle \dfrac{2}{\sqrt{5}}, \dfrac{1}{\sqrt{5}}, 0 \right\rangle$
B. $\dfrac{x-1}{2} = \dfrac{3-y}{1} = \dfrac{2z-1}{4}$		II. $\left\langle -\dfrac{1}{3}, \dfrac{2}{3}, -\dfrac{2}{3} \right\rangle$
C. $\dfrac{x+1}{1} = \dfrac{2y+1}{1}, z = -1$		III. $\left\langle \dfrac{3}{\sqrt{13}}, 0, \dfrac{2}{\sqrt{13}} \right\rangle$
D. $\dfrac{1-x}{1} = \dfrac{y}{2} = \dfrac{1-z}{2}$		IV. $\left\langle \dfrac{2}{3}, -\dfrac{1}{3}, \dfrac{2}{3} \right\rangle$

Choose the correct answer from the options given below:

10 Aug Shift 1

The distance of the plane $\vec{r} \cdot \left(\frac{2}{7}\hat{i} + \frac{3}{7}\hat{j} - \frac{6}{7}\hat{k}\right) = 2$ from the origin is

31st May Shift 2

If the lines $x = ay+b$ , $z = cy+d$ and $x = py+q$ , $z = ry+s$ are perpendicular, then $ap + cr$ is equal to

CUET Mathematics 2026 22nd May Shift 1 PYQs