CUET Mathematics 2026 21st May Shift 2 PYQs

If $\vec a\times\vec b=\vec a\times\vec c$ and $\vec a\neq\vec 0$, then which of the following is/are TRUE?

A. $\vec b=\vec c$

B. $\vec b+\vec c=\vec 0$

C. $\vec b=\vec c+\lambda\vec a$ for some scalar λ

D. $\vec b+\vec c=\lambda\vec a$ for some scalar λ

Choose the correct answer from the options given below:

If $|\vec{a}| = 3$ and $|\vec{b}| = 4$, then a value of $\lambda$ for which $\vec{a} + \lambda \vec{b}$ and $\vec{a} - \lambda \vec{b}$ are perpendicular is :

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

(A) $\vec{a}$ and $\vec{b}$ are perpendicular to each other.

(B) $\vec{a}$ and $\vec{b}$ are parallel.

(C) $|\vec{a}\times\vec{b}| = 2\sqrt{21}$.

(D) Projection of $\vec{a}$ on $\vec{b}$ = 0.

Choose the correct answer from the options given below: