Questions in vectors-m

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	$(2\mathbf{a}+3\mathbf{b})\times (5\mathbf{a}+7\mathbf{b})=$
	If a and b are two vectors such that a . b = 0 and $\mathbf{a}\times \mathbf{b}=\mathbf{0},$ then
	The components of a vector a along and perpendicular to the non-zero vector b are respectively
	$\|\,(\mathbf{a}\times \mathbf{b})\,.\,\mathbf{c}\,\|\,=\,\|\mathbf{a}\|\,\,\|\mathbf{b}\|\,\,\|\mathbf{c}\|,$ if
	Which of the following is not a property of vectors
	The number of vectors of unit length perpendicular to vectors $\mathbf{a}=(1,\,\,1,\,\,0)$ and $\mathbf{b}=(0,\,\,1,\,\,1)$ is
	If $\mathbf{a}=(1,\,\,-1,\,\,1)$ and $\mathbf{c}=(-1,\,\,-1,\,\,0),$ then the vector b satisfying $\mathbf{a}\times \mathbf{b}=\mathbf{c}$ and $\mathbf{a}\,\,.\,\,\mathbf{b}=1$ is
	If $\mathbf{a}\times \mathbf{b}=\mathbf{b}\times \mathbf{c}\ne 0,$ where a, b and c are coplanar vectors, then for some scalar k
	If $\mathbf{a}\ne \mathbf{0},\,\,\mathbf{b}\ne \mathbf{0},\,\,\mathbf{c}\ne \mathbf{0}$, then true statement is
	Let a and b be two non-collinear unit vectors. If $\mathbf{u}=\mathbf{a}-(\mathbf{a}\,.\,\mathbf{b})\,\mathbf{b}$ and $\mathbf{v}=\mathbf{a}\times \mathbf{b},$ then \| v \| is