Short Quiz

Assertion (A) : Projection of \(\vec{a}\) on \(\vec{b}\) is same as projection of \(\vec{b}\) on \(\vec{a}\).
Reason (R) : Angle between \(\overrightarrow{\mathrm{a}}\) and \(\overrightarrow{\mathrm{b}}\) is same as angle between \(\overrightarrow{\mathrm{b}}\) and \(\overrightarrow{\mathrm{a}}\) numerically.

If \(|\overrightarrow{\mathrm{a}}|=2\) and \(-3 \leq \mathrm{k} \leq 2\), then \(|\mathrm{k} \overrightarrow{\mathrm{a}}| \in\) :

For two vectors \(\vec{a}\) and \(\vec{b}\)
Assertion (A) : \(|\vec{a} \times \vec{b}|^2+(\vec{a} \cdot \vec{b})^2=|\vec{a}|^2|\vec{b}|^2\)
Reason (R): : \(|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|=(\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}) \tan \theta,\left(\theta \neq \frac{\pi}{2}\right)\)

If projection of \(\vec{a}=\alpha \hat{i}+\hat{j}+4 \hat{k}\) on \(\vec{b}=2 \hat{i}+6 \hat{j}+3 \hat{k}\) is 4 units, then \(\alpha\) is