CUET Mathematics 2025 16 May Shift 1 PYQs

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

The vector equation of line passing through (2, -1, 3) and perpendicular to the lines

$\frac{x-2}{3} = \frac{y-1}{1} = \frac{z+2}{2}$ and $\frac{x+3}{-4} = \frac{y-5}{-3} = \frac{z+1}{2}$ is

(Here $\lambda$ is a parameter)

Which of the following statements are true?

(A) The vector equation of the line through the point (5, 2, -4) and parallel to the vector $3\hat{i} + 2\hat{j} - 8\hat{k}$ is $\vec{r} = (5\hat{i} + 2\hat{j} - 4\hat{k}) + \lambda(3\hat{i} + 2\hat{j} - 8\hat{k})$

(B) Vector form of the equation of line $\frac{x-5}{3} = \frac{y+4}{7} = \frac{z-6}{2}$ is $\vec{r} = (5\hat{i} - 4\hat{j} + 6\hat{k}) + \lambda(3\hat{i} + 7\hat{j} + 2\hat{k})$

(C) The direction cosines of z-axis are (1, 1,0).

(D) If a line has direction ratios 2, -1, -2, then its direction cosines are -2/3, -1/3, -2/3.

Choose the correct answer from the options given below: