CUET Mathematics - If a line makes angles , , with the positive directions of the coordinate axes, then the value of 2 + 2 + 2 is | PYQs + Solutions

30 May Shift 1

Consider the line $\vec{r} = -2\hat{i} + 3\hat{j} + \hat{k} + \lambda(5\hat{i} - 3\hat{j} - \hat{k})$ . Match List-I with List-II

List-I	List-II
(A) A point on the given line	(I) $\left(\frac{5}{\sqrt{35}}, \frac{-3}{\sqrt{35}}, \frac{-1}{\sqrt{35}}\right)$
(B) Direction ratios of the given line	(II) (2, 3, 1)
(C) Direction cosines of the given line	(III) (5, -3, -1)
(D) Direction ratios of a line perpendicular to given line	(IV) (-2, 3, 1)

Choose the correct answer from the options given below:

22 May Shift 1

If a line makes angle $\pi/3$ and $\pi/4$ with the positive directions of x-axis and y-axis respectively, then the acute angle made by the line with positive direction of z-axis is

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 $\left(\frac{4}{5}, \frac{-3}{5}, \frac{-1}{5}\right)$

(C) It has Direction ratios $\left(2, \frac{-3}{2}, 0\right)$

(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 30 May Shift 2 PYQs

Keyboard Shortcuts