If $a, b$ and $c$ are three vectors such that $|a|=|b|=2$,$a \cdot b=2$ and $a+b+c=0$,then $|c|$ is equal to

$P$ 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

The vectors $a$,$b$,and $a + b$ are:

If the position vectors of the points $A, B, C$ are $i, j, k$ respectively and $P$ is a point such that $\overrightarrow{AB} = \overrightarrow{CP},$ then the position vector of $P$ is

Find the position vector of a point $R$ which divides the line joining two points $P$ and $Q$ whose position vectors are $(2 \vec{a}+\vec{b})$ and $(\vec{a}-3 \vec{b})$ externally in the ratio $1:2$. Also,show that $P$ is the mid-point of the line segment $RQ$.

If the position vectors of the points $A, B, C, D$ are $2i + 3j + 5k, i + 2j + 3k, -5i + 4j - 2k$ and $i + 10j + 10k$ respectively,then: