If the magnitudes of $\bar{a}$,$\bar{b}$ and $\bar{a}+\bar{b}$ are respectively $3$,$4$ and $5$,then the magnitude of $\bar{a}-\bar{b}$ is

If $\bar{a}, \bar{b}, \bar{c}$ are non-zero non-collinear vectors and $\bar{a} \times \bar{b} = \bar{b} \times \bar{c} = \bar{c} \times \bar{a}$,then $\bar{a} + \bar{b} + \bar{c} = $

If three points $A$,$B$,and $C$ have position vectors $(1, x, 3)$,$(3, 4, 7)$,and $(y, -2, -5)$ respectively and if they are collinear,then $(x, y)$ is

The position vectors of $A$ and $B$ are $\vec{a} = \hat{i} - \hat{j} + 2\hat{k}$ and $\vec{b} = 3\hat{i} - \hat{j} + 3\hat{k}$. The position vector of the midpoint of the line segment $AB$ is:

$P$ is the point of intersection of the diagonals of the parallelogram $ABCD$. If $S$ is any point in space and $\vec{SA} + \vec{SB} + \vec{SC} + \vec{SD} = \lambda \vec{SP}$, then $\lambda$ equals

If the position vector of a point $A$ is $a + 2b$ and a point $P$ divides $AB$ in the ratio $2:3$,where the position vector of $P$ is $a$,then the position vector of $B$ is: