CUET Mathematics 2025 16 May Shift 1 PYQs

If $\theta$ is an acute angle and the vector $\vec{a} = (\sin \theta)\vec{i} + (\cos\theta)\vec{j}$ is perpendicular to the vector $\vec{b} = [i - \sqrt{3}j]$ then $\theta$ is equal to

Which of the following statements are true?

(A) If $\vec{r} = x\vec{i} + y\vec{j} + z\vec{k}$, then $x, y, z$ are called direction ratios of $\vec{r}$.

(B) For any two vectors $\vec{a}$ and $\vec{b}$, $\vec{a} + \vec{b} = \vec{b} + \vec{a}$

(C) $\vec{a} \perp \vec{b}$ if and only if $\vec{a} \times \vec{b} = \vec{0}$

(D) Projection of $\vec{b}$ on $\vec{a}$ is $\frac{\vec{a} \cdot \vec{b}}{|\vec{a}|^2}$

Choose the correct answer from the options given below:

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