CUET Mathematics 2026 22nd May Shift 2 PYQs

A vector $\vec{a}$ of magnitude $3\sqrt{2}$ making an angle of $\frac{\pi}{3}$ with $\hat{i}$, $\frac{\pi}{4}$ with $\hat{j}$ and an actue angle $\theta$ with $\hat{k}$, is

If $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ and $|\vec{a}| = 5, |\vec{b}| = 3, |\vec{c}| = 7$, then the acute angle between $\vec{a}$ and $\vec{b}$ is

If $\vec{a},\vec{b}$ and $\vec{c}$ are three vectors such that $\lvert \vec{a} \rvert=\frac{1}{\sqrt{2}}$, $\lvert \vec{b} \rvert=\frac{1}{\sqrt{3}}$, $\lvert \vec{c} \rvert=\frac{1}{\sqrt{6}}$, $\lvert \vec{a}+\vec{b}+\vec{c} \rvert=1$ and $\vec{c}=\lambda(\vec{a}\times\vec{b})$. The angle between $\vec{a}$ and $\vec{b}$ is