The three vectors $\vec{A}=3 \hat{i}-2 \hat{j}+\hat{k}$,$\vec{B}=\hat{i}-3 \hat{j}+5 \hat{k}$ and $\vec{C}=2 \hat{i}-\hat{j}+4 \hat{k}$ will form

If $\vec{A}=\hat{i}+\hat{j}+3 \hat{k}$,$\vec{B}=-\hat{i}+\hat{j}+4 \hat{k}$ and $\vec{C}=2 \hat{i}-2 \hat{j}-8 \hat{k}$,then the angle between the vectors $\vec{P}=\vec{A}+\vec{B}+\vec{C}$ and $\vec{Q}=(\vec{A} \times \vec{B})$ is (in degree) (in $^{\circ}$)

If $P = Q = R$ and $\vec{P} + \vec{Q} = \vec{R}$,let $\theta_1$ be the angle between $\vec{P}$ and $\vec{R}$. If $\vec{P} + \vec{Q} + \vec{R} = \vec{0}$,let $\theta_2$ be the angle between $\vec{P}$ and $\vec{R}$. What is the relationship between $\theta_1$ and $\theta_2$?

Match Column-$I$ with Column-$II$.

Column-$I$	Column-$II$
$(1)$ Resultant of two mutually perpendicular vectors	$(a)$ Along the bisector of the angle between them
$(2)$ Direction of $\overrightarrow A \times \overrightarrow B$	$(b)$ Coplanar
	$(c)$ Perpendicular to the plane containing $\overrightarrow A$ and $\overrightarrow B$

$A$ man travels $30 \ m$ along the direction of $3 \hat{i} + 4 \hat{j}$ and then moves '$d$' meters perpendicular to the initial direction such that his total displacement is along the $x$-axis. What is the value of '$d$' in meters?

$100$ coplanar forces,each equal to $10 \ N$,act on a body. Each force makes an angle of $\pi/50$ radians with the preceding force. What is the resultant of the forces in $N$?