Three Dimensional Geometry: 2 marks Questions (CBSE Class 12)

Find the co-ordinates of the point on the line $\vec{r}=-\hat{j}+3\hat{k}+\lambda (2\hat{i}-2\hat{j}+\hat{k})$ such that the sum of co-ordinates is 3.

Find the co-ordinates of foot of perpendicular drawn from (0, 0, 0) to line $\frac{x}{1}=\frac{y+1}{-1}=\frac{z-3}{-2}$.

Find the co-ordinates of the point on line $x=\frac{y-1}{2}=\frac{z-2}{3}$ whose y co-ordinate is 3 times the $x$ co-ordinate.

If the lines $\frac{x-3}{1}=\frac{1-y}{1}=\frac{z+2}{p}$ and $\frac{2-x}{3}=\frac{y+1}{5}=\frac{z+56}{2p}$ are perpendicular to each other, then find the value(s) of p.

Find the vector equation of a line passing through the origin and perpendicular to both the lines $\vec{r}=2\hat{i}-\hat{j}+2\hat{k}+\lambda (3\hat{i}+4\hat{j}+2\hat{k})$ and $\vec{r}=\mu (\hat{i}-\hat{j}+\hat{k})$.

Find the angle between the following pair of lines :
$\frac{x-2}{3}=\frac{y+5}{2}=\frac{1-z}{-6}$ and
$\frac{x-7}{1}=\frac{y}{2}=\frac{6-z}{-2}$