CUET Mathematics 2026 30th May Shift 1 PYQs

If $\vec{a}=2\hat{i}+\hat{j}$, and $\vec{b}=\hat{j}-\hat{k}$, then which of the following statements is/are TRUE ?

A. $|\vec{a}+\vec{b}|=3$

B. Unit vector along $\vec{a}+\vec{b}$ is $2\hat{i}+2\hat{j}-\hat{k}$

C. Direction ratio of $\vec{a}+\vec{b}$ are 2, 2, -1

D. unit vector perpendicular to $\vec{a}$ and $\vec{b}$ is $-\frac{1}{3}\hat{i}+\frac{2}{3}\hat{j}+\frac{2}{3}\hat{k}$

Choose the correct answer from the options given below:

The value of $\lambda$, for which the two vectors $2\hat{i} - \hat{j} + 2\hat{k}$ and $3\vec{i} + \lambda\vec{j} + \hat{k}$ are perpendicular, is:

The position vector of a point R which divides the line joining two points P and Q whose position vectors are $\hat{i} + 2\hat{j} - \hat{k}$ and $-\hat{i} + \hat{j} + \hat{k}$ respectively in the ratio 2 : 1 externally is :