CUET Mathematics 2025 22 May Shift 1 PYQs

The value of $x$ so that the lines $\frac{1-x}{3} = \frac{7y-14}{24} = \frac{z-3}{2}$ and $\frac{7-7x}{3x} = \frac{y-5}{1} = \frac{6-z}{5}$ are at right angle, is:

If a line makes angles $\alpha, \beta, \gamma$ with the positive directions of the coordinate axes, then the value of $\cos 2\alpha + \cos 2\beta + \cos 2\gamma$ is

The acute angle between the lines $\vec{r} = (4\hat{i} - \hat{j}) + \lambda(2\hat{i} + \hat{j} - 3\hat{k})$ and $\frac{x-1}{1} = \frac{y+1}{-3} = \frac{z-2}{2}$ is