If a unit vector is represented by $\vec{U} = 0.9\hat{i} - 0.2\hat{j} + m\hat{k}$, then the value of $m$ is

If the vector $\overrightarrow{A} = 2\hat{i} + 4\hat{j} - 5\hat{k}$,find its direction cosines.

If three vectors along coordinate axes represent the adjacent sides of a cube of length $b$,then the unit vector along its diagonal passing through the origin will be

Two vectors of same magnitude act at a point. Twice the product of the magnitudes of two vectors is equal to the square of the magnitude of their resultant. The angle between the two vectors is (in $^{\circ}$)

The vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ lie in a plane. Another vector $\overrightarrow{C}$ lies outside this plane. The resultant $\overrightarrow{R} = \overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C}$ of these three vectors:

$A$ particle moves from point $P (2, 3, 5)$ to point $Q (3, 4, 5)$. The displacement vector is: