Questions in vectors-m

Select	Question
	The projection of the vector $2\mathbf{i}+\mathbf{j}-3\mathbf{k}$ on the vector $\mathbf{i}-2\mathbf{j}+\mathbf{k}$is_______
	If $\|\mathbf{a}\|=\|\mathbf{b}\|=1$ and $\mathbf{\|a}+\mathbf{b}\|=\sqrt{3}$, then the value of $(3\mathbf{a}-4\mathbf{b}).(2\mathbf{a}+5\mathbf{b})$ is
	A unit vector in the plane of $\mathbf{i}+2\mathbf{j}+\mathbf{k}$ and $\mathbf{i}+\mathbf{j}+2\mathbf{k}$are perpendicular to $2\mathbf{i}+\mathbf{j}+\mathbf{k}$is
	If $\mathbf{a},\mathbf{b}$ and $\mathbf{c}$ are perpendicular to $\mathbf{b}+\mathbf{c},\mathbf{c}+\mathbf{a}$and $\mathbf{a}+\mathbf{b}$ respectively and if $\|\mathbf{a}+\mathbf{b}\|=6,\|\mathbf{b}+\mathbf{c}\|=8$ and $\|\mathbf{c}+\mathbf{a}\|=10$ then $\|\mathbf{a}+\mathbf{b}+\mathbf{c}\|=$
	If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are any vectors, then the true statement is
	If a and b are unit vectors such that $\mathbf{a}\times \mathbf{b}$ is also a unit vector, then the angle between a and b is
	The points $A\,(\mathbf{a}),\,B\,(\mathbf{b}),\,C\,(\mathbf{c})$ will be collinear if
	$(\mathbf{a}-\mathbf{b})\times (\mathbf{a}+\mathbf{b})=$
	If $\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0},$ then which relation is correct
	If $\theta$ be the angle between the vectors a and b and $\|\mathbf{a}\times \mathbf{b}\|\,=\mathbf{a}\,.\,\mathbf{b},$ then $\theta =$