Questions in vectors-m

Select	Question
	If the angle between two vectors $\mathbf{i}+\mathbf{k}$ and $\mathbf{i}-\mathbf{j}+a\mathbf{k}$ is $\pi /3,$ then the value of $a=$
	If three vectors a, b, c satisfy $\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}$ and $\|\mathbf{a}\|\,\,=\,\,3,\,$ $\|\mathbf{b}\|\,=5,$ $\|\mathbf{c}\|\,\,=7,$ then the angle between a and b is
	If a, b and c are unit vectors such that $\mathbf{a}+\mathbf{b}-\mathbf{c}=0,$ then the angle between a and b is
	If the sum of two unit vectors is a unit vector, then the magnitude of their difference is
	The angle between the vector $2i+3j+k$ and $2i-j-k$ is
	If $\theta $ be the angle between the vectors $\mathbf{a}=2\mathbf{i}+2\mathbf{j}-\mathbf{k}$ and $\mathbf{b}=6\mathbf{i}-3\mathbf{j}+2\mathbf{k}$, then
	If a and b are two unit vectors such that $\mathbf{a}+2\,\mathbf{b}$ and $5a-4b$ are perpendicular to each other, then the angle between a and b is
	Let a and b be two unit vectors inclined at an angle $\theta $, then $\sin \,(\theta /2)$ is equal to
	The angle between the vectors a + b and a – b, when $\mathbf{a}=(1,\,1,\,4)$ and $b=(1,\,-1,\,4)$ is
	A vector of length 3 perpendicular to each of the vectors $3\,\mathbf{i}+\mathbf{j}-4\,\mathbf{k}$ and $6\,\mathbf{i}+5\,\mathbf{j}-2\,\mathbf{k}$ is