CUET Mathematics 2026 18th May Shift 1 PYQs

If $P(\vec{r})$ is a position vector of a point with scalar components $(x,y,z)$, then the value of $(\vec{r}.\hat{i})(-\hat{i})-(\vec{r}.\hat{j})\hat{j}+(\vec{r}.(-\hat{k}))\hat{k}$, is:

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:

The vector $\{(a^2+a-2)\hat{i}+(a^2-4)\hat{j}-(a^2-5a+6)\hat{k}\}$ makes acute angles with coordinate axes, then values of $a$ lies in :