If $a, b$ and $c$ are unit vectors such that $a+b+c=0$,then the angle between $a$ and $b$ is

Let $\overline{a}, \overline{b}$,and $\overline{c}$ be three non-zero vectors such that no two of these are collinear. If the vector $\overline{a}+2\overline{b}$ is collinear with $\overline{c}$ and $\overline{b}+3\overline{c}$ is collinear with $\overline{a}$,then $\overline{a}+2\overline{b}+6\overline{c}$ equals

Let $a, b$ and $c$ be three non-coplanar vectors. The vector equation of a line which passes through the point of intersection of two lines,one joining the points $a+2b-5c$ and $-a-2b-3c$,and the other joining the points $-4c$ and $6a-4b+4c$,is

If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that $\vec{a}+\vec{b}+\sqrt{3} \vec{c}=\overrightarrow{0}$,then the angle between $\vec{a}$ and $\vec{b}$ is

If $a$ and $b$ are unit vectors and $\theta$ $(0 < \theta < \pi)$ is the angle between them, then the value of $|a + b| / |a - b|$ is equal to

Find the distance between the lines $l_{1}$ and $l_{2}$ given by $\vec{r}=\hat{i}+2 \hat{j}-4 \hat{k}+\lambda(2 \hat{i}+3 \hat{j}+6 \hat{k})$ and $\vec{r}=3 \hat{i}+3 \hat{j}-5 \hat{k}+\mu(2 \hat{i}+3 \hat{j}+6 \hat{k})$.