Two vectors $P = 2\hat{i} + b\hat{j} + 2\hat{k}$ and $Q = \hat{i} + \hat{j} + \hat{k}$ will be parallel if $b=$ ........

The values of $x$ and $y$ for which vectors $\vec{A} = (6 \hat{i} + x \hat{j} - 2 \hat{k})$ and $\vec{B} = (5 \hat{i} + 6 \hat{j} - y \hat{k})$ are parallel are

If the vector $\vec{P} = 3\hat{i} + 4\hat{j} + 12\hat{k}$,then the magnitude of the vector $\vec{P}$ is ......

$A$ vector $\vec{A}$ is rotated by a small angle $\Delta \theta$ radian $(\Delta \theta \ll 1)$ to get a new vector $\vec{B}$. In that case,$|\vec{B} - \vec{A}|$ is

The vectors $(A + B)$ and $(A - B)$ are at right angles to each other. This is possible under the condition

The magnitude of a given vector with end points $(4, -4, 0)$ and $(-2, -2, 0)$ is: