Given $A = \hat{i} + \hat{j} + \hat{k}$ and $B = -\hat{i} - \hat{j} - \hat{k}$,then the angle between $(A - B)$ and $A$ is: (in $^{\circ}$)

The resultant of two vectors $\vec{P}$ and $\vec{Q}$ is $\vec{R}$. If $\vec{Q}$ is doubled,the new resultant vector is perpendicular to $\vec{P}$. What is the magnitude of $\vec{R}$?

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is . . . . . . (in $^{\circ}$)

If $\vec{a}$ and $\vec{b}$ are two unit vectors inclined at an angle of $60^{\circ}$ to each other,then:

Two vectors $\vec{A}$ and $\vec{B}$ have equal magnitudes. Then the vector $\vec{A} + \vec{B}$ is perpendicular to:

The vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$. The angle between the two vectors is: (in $^{\circ}$)