Short Quiz

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

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 \(\vec{a}=2 \hat{i}-\hat{j}+\hat{k}\) and \(\vec{b}=\hat{i}+\hat{j}-\hat{k}\), then \(\vec{a}\) and \(\vec{b}\) are:

For any two vectors \(\overrightarrow{\mathrm{a}}\) and \(\overrightarrow{\mathrm{b}}\), which of the following statements is always true?