Questions in vectors-m

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	The perimeter of the triangle whose vertices have the position vectors $(\mathbf{i}+\mathbf{j}+\mathbf{k}),\,\,(5\mathbf{i}+3\mathbf{j}-3\mathbf{k})$ and $(2\mathbf{i}+5\mathbf{j}+9\mathbf{k}),$ is given by
	The position vectors of two points A and B are $\mathbf{i}+\mathbf{j}-\mathbf{k}$ and $2\mathbf{i}-\mathbf{j}+\mathbf{k}$ respectively. Then $\|\overrightarrow{AB}\|\,\,=$
	The magnitudes of mutually perpendicular forces a, b and c are 2, 10 and 11 respectively. Then the magnitude of its resultant is
	The system of vectors $\mathbf{i},\,\,\mathbf{j},\,\,\mathbf{k}$ is
	The direction cosines of the resultant of the vectors $(\mathbf{i}+\mathbf{j}+\mathbf{k}),$ $(-\mathbf{i}+\mathbf{j}+\mathbf{k}),$ $(\mathbf{i}-\mathbf{j}+\mathbf{k})$ and $(\mathbf{i}+\mathbf{j}-\mathbf{k}),$ are
	The position vectors of P and Q are $5\mathbf{i}+4\mathbf{j}+a\mathbf{k}$ and $-\mathbf{i}+2\mathbf{j}-2\mathbf{k}$ respectively. If the distance between them is 7, then the value of a will be
	A zero vector has
	A unit vector a makes an angle $\frac{\pi }{4}$ with z-axis. If $\mathbf{a}+\mathbf{i}+\mathbf{j}$ is a unit vector, then a is equal to
	A force is a
	If $\mathbf{a}, \mathbf{b}, \mathbf{c}, \mathbf{d}$ be the position vectors of the points A, B, C and D respectively referred to same origin O such that no three of these points are collinear and $\mathbf{a}+\mathbf{c}=\mathbf{b}+\mathbf{d},$ then quadrilateral ABCD is a