Find the coordinates of the foot of the perpendicular drawn from the point $A(1, 2, 1)$to the line joining the points $B(1, 4, 6) and C(5, 4, 4).$

Find the coordinates of the foot of the perpendicular drawn from the point $A(1, 8, 4)$to the line joining the points $B(0, -1, 3) and C(2, -3, -1)$.

Find the image of the point $(0, 2, 3)$ in the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$

Find the image of the point $(5, 9, 3)$ in the line $\frac{x-1}{2}=\frac{y=2}{3}=\frac{z-3}{4}$

Find the image of the point $(2, -1, 5)$ in the line

$\overrightarrow{r}=(1\hat{i}-2\hat{j}-8\hat{k})+\lambda (10\hat{i}-4\hat{j}-11\hat{k})$

Show that the points$A(2, 1, 3), B(5, 0, 5)$and $C(-4,3,-1)$ are collinear.

Show that the points$A(2, 3, -4), B(1, -2, 3)$ and $C(3, 8, -11)$are collinear.

Find the value of $\lambda$ for which the points $A(2, 5, 1), B(1, 2, -1)$ and$C(3, \lambda , 3)$ are collinear.

Find the values of $\lambda$ and μ so that the points $A(3, 2, -4)$, $B(9, 8, -10)$ and$C(\lambda , \mu -6)$ are collinear.