Questions in vectors-m

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	If $\mathbf{r}\,.\,\mathbf{i}=\mathbf{r}\,.\,\mathbf{j}=\mathbf{r}\,.\,\mathbf{k}$ and $\|\mathbf{r}\|\,\,=3,$ then $\mathbf{r}=$
	If a, b, c are non-zero vectors such that $\mathbf{a}\,\,.\,\,\mathbf{b}=\mathbf{a}\,\,.\,\,\mathbf{c},$ then which statement is true
	If a and b be unlike vectors, then a . b =
	If a, b, c are unit vectors such that $\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0},$ then $\mathbf{a}\,\,.\,\,\mathbf{b}+\mathbf{b}\,\,.\,\,\mathbf{c}+\mathbf{c}\,\,.\,\,\mathbf{a}=$
	If a, b, c are mutually perpendicular vectors of equal magnitudes, then the angle between the vectors a and $\mathbf{a}+\mathbf{b}+\mathbf{c}$ is
	If a, b, c are mutually perpendicular unit vectors, then $\|\mathbf{a}+\mathbf{b}+\mathbf{c}\|\,\,=$
	If $\|\mathbf{a}\|+\|\mathbf{b}\|\,=\,\|\mathbf{c}\|$ and $\mathbf{a}+\mathbf{b}=\mathbf{c},$ then the angle between a and b is
	If a has magnitude 5 and points north-east and vector b has magnitude 5 and points north-west, then $\|\,\,\mathbf{a}-\mathbf{b}\,\,\|\,=$
	If $\theta$ be the angle between the unit vectors a and b, then $\cos \frac{\theta }{2}=$
	If $\|\mathbf{a}\|\,=3,\,\,\|\mathbf{b}\|\,=4,\,\,\|\mathbf{c}\|\,=\,\,5$ and $\mathbf{a}+\mathbf{b}+\mathbf{c}=0,$ then the angle between a and b is