If $|a| = 3, |b| = 4$ and $|a + b| = 5,$ then $|a - b| = $

Classify the following as scalar and vector quantities:
Force

If a unit vector lies in the $yz$-plane and makes angles of $30^\circ$ and $60^\circ$ with the positive $y$-axis and $z$-axis respectively,then its components along the coordinate axes are:

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are unit vectors and $|\overrightarrow{a}+\overrightarrow{b}|=1$,then $|\overrightarrow{a}-\overrightarrow{b}|$ is equal to

The direction cosines of the vector $\vec{a} = -2 \hat{i} + \hat{j} - 5 \hat{k}$ are

Let $u$ and $v$ be two vectors in a plane. Then any vector $w$ in the plane can be written as $w = au + bv$ for some scalars $a$ and $b$ if and only if