Questions in vectors-m

Select	Question
	If $\mathbf{a}\ne \mathbf{0},\,\,\mathbf{b}\ne \mathbf{0}$ and $\|\mathbf{a}+\mathbf{b}\|\,=\,\|\mathbf{a}-\mathbf{b}\|,$ then the vectors a and b are
	The vector $2\,\mathbf{i}+a\,\mathbf{j}+\mathbf{k}$ is perpendicular to the vector $2\,\mathbf{i}-\mathbf{j}-k,$ if $a=$
	If $\mathbf{a}=2\,\mathbf{i}+2\,\mathbf{j}+3\,\mathbf{k},\,\,\mathbf{b}=-\mathbf{i}+2\,\mathbf{j}+\mathbf{k}$ and $c=3\,\mathbf{i}+\mathbf{j},$ then $\mathbf{a}+t\,\mathbf{b}$ is perpendicular to c if $t=$
	The vector $2\,\mathbf{i}+\mathbf{j}-\mathbf{k}$ is perpendicular to $\mathbf{i}-4\mathbf{j}+\lambda \mathbf{k},$ if $\lambda =$
	The vectors $2\,\mathbf{i}+3\,\mathbf{j}-4\,\mathbf{k}$ and $a\,\mathbf{i}+b\,\mathbf{j}+c\,\mathbf{k}$ are perpendicular, when
	A unit vector in the $xy-$plane which is perpendicular to $4\mathbf{i}-3\mathbf{j}+\mathbf{k}$ is
	If $l\,\mathbf{a}+m\,\mathbf{b}+n\,\mathbf{c}=\mathbf{0},$ where $l,\,m,\,\,n$ are scalars and a, b, c are mutually perpendicular vectors, then
	The unit normal vector to the line joining $\mathbf{i}-\mathbf{j}$ and $2\,\mathbf{i}+3\,\mathbf{j}$ and pointing towards the origin is
	If the vectors $a\,\mathbf{i}-2\mathbf{j}+3\mathbf{k}$ and $3\mathbf{i}+6\mathbf{j}-5\mathbf{k}$ are perpendicular to each other, then a is given by
	The value of $\lambda $ for which the vectors $2\lambda \mathbf{i}+\mathbf{j}-\mathbf{k}$ and $2\mathbf{j}+\mathbf{k}$ are perpendicular, is