Questions in vectors-m

Select	Question
	If $\mathbf{a}\times \mathbf{b}=\mathbf{b}\times \mathbf{c}\ne 0$ and $\mathbf{a}+\mathbf{c}\ne 0,$ then
	A unit vector perpendicular to the plane determined by the points (1, – 1, 2), (2, 0, – 1) and (0, 2, 1) is
	If $\mathbf{a}=2\mathbf{i}+3\mathbf{j}-5\mathbf{k},\,\,\mathbf{b}=m\mathbf{i}+n\mathbf{j}+12\mathbf{k}$ and $\mathbf{a}\times \mathbf{b}=0,$ then $(m,\,\,n)=$
	A unit vector which is perpendicular to $\mathbf{i}+2\mathbf{j}-2\mathbf{k}$ and $-\mathbf{i}+2\mathbf{j}+2\mathbf{k}$ is
	If $A\,(-1,\,\,2,\,\,3),\,\,B\,(1,\,\,1,\,\,1)$ and $C\,(2,\,\,-1,\,\,3)$ are points on a plane. A unit normal vector to the plane ABC is
	The unit vector perpendicular to the vectors $6\mathbf{i}+2\mathbf{j}+3\mathbf{k}$ and $3\mathbf{i}-6\mathbf{j}-2\mathbf{k},$ is
	For any two vectors a and b, ${{(\mathbf{a}\times \mathbf{b})}^{2}}$ is equal to
	The unit vector perpendicular to $3\mathbf{i}+2\mathbf{j}-\mathbf{k}$ and $12\mathbf{i}+5\mathbf{j}-5\mathbf{k},$ is
	The sine of the angle between the two vectors $3\mathbf{i}+2\mathbf{j}-\mathbf{k}$ and $12\mathbf{i}+5\mathbf{j}-5\mathbf{k}$ will be
	For any two vectors a and b, if $\mathbf{a}\times \mathbf{b}=\mathbf{0},$ then