CUET Mathematics 2026 22nd May Shift 1 PYQs

Let $\vec{a} = 2\hat{i} + 3\hat{j} - 4\hat{k}$ and $\vec{b} = 3\hat{i} - 5\hat{j} + 6\hat{k}$. Let $\vec{c}$ be a vector such that $\vec{c} \times \vec{a} = \vec{b} \times \vec{c}$ and $\vec{c}\cdot(2\vec{a}-3\vec{b}) = 238\sqrt{2}$ then $|\vec{c}|^2$ is equal to :

Which of the following statements are correct?

(A) $\hat{i} \times (\hat{j} \times \hat{k}) = \vec{0}$.

(B) If $|\vec{a}\times\vec{b}|=2$, $\vec{a}.\vec{b}=4$, then $|\vec{a}|^2|\vec{b}|^2=6$.

(C) The number of vectors of unit length perpendicular to $\vec{a}$ and $\vec{b}$ are 2.

(D) If $\vec{a}$ and $\vec{b}$ represent the diagonals of the rhombus, then $\vec{a}.\vec{b}=0$

Choose the correct answer from the options given below:

Let $\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} - \hat{j} + 2\hat{k}$ be two vectors. Then which of the following are TRUE?

A. $\vec{a}$ and $\vec{b}$ are perpendicular

B. Projection of $\vec{a}$ on $\vec{b}$ is 1

C. $|\vec{a} \times \vec{b}| = 3\sqrt{13}$

D. $\vec{a} - \vec{b}$ is a unit vector

Choose the correct answer from the options given below: