If the angle between $\vec{a}$ and $\vec{b}$ is $30^o$,then the angle between $3\vec{a}$ and $-4\vec{b}$ will be ............ $^o$.

State whether the following statement is true or false:
Two vectors having the same magnitude are collinear.

If $P$ divides the line segment joining the points $A$ and $B$ in the ratio $2:1$ and the position vectors of $A$ and $B$ are $\hat{i}-2\hat{j}$ and $-3\hat{i}+5\hat{j}$ respectively,then the position vector of $P$ is

If $a$ and $b$ are the position vectors of $A$ and $B$ respectively,then the position vector of a point $C$ on $AB$ produced such that $\overrightarrow{AC} = 3\overrightarrow{AB}$ is

Suppose that $\vec{p}, \vec{q}$ and $\vec{r}$ are three non-coplanar vectors in $\mathbb{R}^3$. Let the components of a vector $\vec{s}$ along $\vec{p}, \vec{q}$ and $\vec{r}$ be $4, 3$ and $5$,respectively. If the components of this vector $\vec{s}$ along $(-\vec{p}+\vec{q}+\vec{r}), (\vec{p}-\vec{q}+\vec{r})$ and $(-\vec{p}-\vec{q}+\vec{r})$ are $x, y$ and $z$,respectively,then the value of $2x+y+z$ is

If $a = \hat{i} + 2 \hat{j} + 3 \hat{k}$,$b = 2 \hat{i} + 3 \hat{j} + \hat{k}$,$c = 8 \hat{i} + 13 \hat{j} + 9 \hat{k}$ and $x a + y b + z c = 0$,then $\frac{x y}{z^2} =$