Vector Algebra PYQs - Last 5 Years

If a vector $\vec{v}=3 \hat{i}$ is rotated in the $x-z$ plane by an angle $\theta$ with respect to $x$－axis in the clockwise direction，then for an observer at $+y$ axis the vector will be

Three vectors $\vec{a}, \vec{b}$ and $\vec{c}$ are such that $|\vec{a}|=1,|\vec{b}|=2$ and $|\vec{c}|=4$ along with $\vec{a}+\vec{b}+\vec{c}=0$ ．Then，the value of $4 \vec{a} \cdot \vec{b}+3 \vec{b} \cdot \vec{c}+3 \vec{c} \cdot \vec{a}$ wil...

Six vectors $\vec{a}, \vec{b}, \vec{c}, \vec{d}, \vec{e}$ and $\vec{f}$ have the magnitudes and directions indicated in the figure. Which of the following statements is true?

Let \(\theta\) be the angle between two vectors \(\vec{A}\) and \(\vec{B}\). If \(\hat{a}_{\perp}\) is the unit vector perpendicular to \(\vec{A}\), then the direction of $$
\overrightarrow{\mathrm{B}}-\mathrm{B} \sin \theta \hat{\mathrm{a}...