Questions in vectors-m

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	If a and b are two vectors, then ${{(\mathbf{a}\times \mathbf{b})}^{2}}$ equals
	For any vectors a, b, c $\mathbf{a}\times (\mathbf{b}+\mathbf{c})+\mathbf{b}\times (\mathbf{c}+\mathbf{a})+\mathbf{c}\times (\mathbf{a}+\mathbf{b})=$
	If $\mathbf{a}\,.\,\mathbf{b}=\mathbf{a}\,.\,\mathbf{c},\,\,\mathbf{a}\,\times \mathbf{b}=\mathbf{a}\times \mathbf{c}$ and $\mathbf{a}\ne \mathbf{0},$ then
	If $\|\mathbf{a}\|\,=2,\,\,\|\mathbf{b}\|\,=5$ and $\|\mathbf{a}\times \mathbf{b}\|\,=8,$ then a . b is equal to
	If $\|\mathbf{a}\,.\,\mathbf{b}\|\,=3$ and $\|\mathbf{a}\times \mathbf{b}\|\,=4,$ then the angle between a and b is
	If $\mathbf{a}=2\mathbf{i}+2\mathbf{j}-\mathbf{k}$ and $\mathbf{b}=6\mathbf{i}-3\mathbf{j}+2\mathbf{k},$ then the value of $\mathbf{a}\times \mathbf{b}$ is
	The scalars l and m such that $l\mathbf{a}+m\mathbf{b}=\mathbf{c},$ where a, b and c are given vectors, are equal to
	$\|\mathbf{a}\times \mathbf{i}{{\|}^{2}}+\|\mathbf{a}\times \mathbf{j}{{\|}^{2}}+\|\mathbf{a}\times \mathbf{k}{{\|}^{2}}=$
	A unit vector perpendicular to the plane determined by the points $P\,(1,\,\,-1,\,\,2),\,\,Q\,(2,\,\,0,\,-1)$ and $R\,(0,\,\,2,\,\,1)$ is
	A unit vector perpendicular to the vector $4\mathbf{i}-\mathbf{j}+3\mathbf{k}$ and $-2\mathbf{i}+\mathbf{j}-2\mathbf{k}$ is