If the position vectors of the vertices $A, B, C$ of a triangle $ABC$ are $7j + 10k$,$-i + 6j + 6k$,and $-4i + 9j + 6k$ respectively,then the triangle is:

$a, b, c$ are non-coplanar vectors. If $a+3 b+4 c=x(a-2 b+3 c)+y(a+5 b-2 c)+z(6 a+14 b+4 c)$,then $x+y+z=$

If $D, E$ and $F$ are respectively mid-points of $AB, AC$ and $BC$ in $\triangle ABC$,then $\overrightarrow{BE} + \overrightarrow{AF}$ is equal to

The projection of $\hat{i}-\hat{j}$ on $\hat{i}+\hat{j}$ is . . . . . . .

Let $O$ be the origin,$\vec{OP} = \vec{a}$ and $\vec{OQ} = \vec{b}$. If $R$ is the point on $\vec{OP}$ such that $\vec{OP} = 5\vec{OR}$,and $M$ is the point such that $\vec{OQ} = 5\vec{RM}$,then $\vec{PM}$ is equal to:

If the vector $19 \hat{i}+22 \hat{j}+5 \hat{k}$ bisects an angle between the vectors $a$ and $6 \hat{i}+8 \hat{j}$,then the unit vector in the direction of $a$ is