Questions in vectors-m

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	A vector whose modulus is $\sqrt{51}$ and makes the same angle with $\mathbf{a}=\frac{\mathbf{i}-2\mathbf{j}+2\mathbf{k}}{3},\,\,\mathbf{b}=\frac{-\,4\mathbf{i}-3\mathbf{k}}{5}$ and $\mathbf{c}=\mathbf{j},$ will be
	If a, b, c are coplanar vectors, then
	If $\vec{\lambda }$ is a unit vector perpendicular to plane of vector a and b and angle between them is $\theta$, then a . b will be
	If $\mathbf{p}=\mathbf{i}-2\mathbf{j}+3\mathbf{k}$ and $\mathbf{q}=3\mathbf{i}+\mathbf{j}+2\mathbf{k},$ then a vector along r which is linear combination of p and q and also perpendicular to q is
	If $\mathbf{d}=\lambda \,(\mathbf{a}\times \mathbf{b})+\mu \,(\mathbf{b}\times \mathbf{c})+\nu \,(\mathbf{c}\times \mathbf{a})$and $[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]=\frac{1}{8},$ then $\lambda +\mu +\nu $ is equal to
	The horizontal force and the force inclined at an angle ${{60}^{o}}$ with the vertical, whose resultant is in vertical direction of P kg, are
	If a and b are mutually perpendicular vectors, then ${{(\mathbf{a}+\mathbf{b})}^{2}}=$
	$\mathbf{a}\,.\,\mathbf{b}=0,$ then
	If $\|\mathbf{a}\|\,\,=3,\,\,\,\|\mathbf{b}\|\,\,=1,\,\,\|\mathbf{c}\|\,\,=4$ and $\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0},$ then $\mathbf{a}\,.\,\mathbf{b}+\mathbf{b}\,.\,\mathbf{c}+\mathbf{c}\,.\,\mathbf{a}=$
	If ABCDEF is regular hexagon, the length of whose side is a, then $\overrightarrow{AB}\,\,.\,\overrightarrow{AF}+\frac{1}{2}\,{{\overrightarrow{BC}}^{2}}=$