What should be the angle $\theta$ between two vectors $\vec{A}$ and $\vec{B}$ so that the magnitude of the resultant vector $\vec{R}$ is maximum (in $^{\circ}$)?

Which of the following dopant is $NOT$ used in $Ge$ to obtain $n$-type semiconductor?

The angle subtended by the vector $\vec{A} = 4 \hat{i} + 3 \hat{j} + 12 \hat{k}$ with the $x$-axis is

If $|\vec{v}_1 + \vec{v}_2| = |\vec{v}_1 - \vec{v}_2|$ and $\vec{v}_1$ and $\vec{v}_2$ are finite,then:

Given: $\vec{A} = 2\hat{i} + p\hat{j} + q\hat{k}$ and $\vec{B} = 5\hat{i} + 7\hat{j} + 3\hat{k}$. If $\vec{A} \parallel \vec{B}$,then the values of $p$ and $q$ are,respectively:

$\vec{A}$ and $\vec{B}$ are two non-zero vectors inclined at an angle $\theta$. $\hat{a}$ and $\hat{b}$ are unit vectors along $\vec{A}$ and $\vec{B}$ respectively. The component of $\vec{A}$ in the direction of $\vec{B}$ is