CUET Mathematics 2025 13 May Shift 1 PYQs

A unit vector perpendicular to the vectors $\hat{i} - \hat{j}$ and $\hat{i} + \hat{j}$ is

If the vectors $\vec{a} = 3\hat{i} - p\hat{j} + 5\hat{k}$ and $\vec{b} = -6\hat{i} + 14\hat{j} + q\hat{k}$ are collinear, then the value of p and q are:

Let $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$ and $\vec{b} = -2\hat{i} + 3\hat{j} - 4\hat{k}$, then which of the following statements are correct?

(A) $|\vec{a}| = \sqrt{14}$

(B) $|\vec{b}| = 29$

(C) $\vec{a} \cdot \vec{b} = 8$

(D) Angle between $\vec{a}$ and $\vec{b}$ is $\cos^{-1}\left(\frac{-8}{\sqrt{406}}\right)$

Choose the correct answer from the options given below: