Question

Find the co-ordinate of the pt. $p$, if $\ell \left(PQ\right)=21$, $Q\equiv (-2,1,-8)$ and directional cosines of $PQ$ are $\left(6/7\right),\left(2/7\right),\left(3/7\right)$?

Answer 1

$l\left(PQ\right)=21,Q=(-2,1,-8)(l,m,n)=\frac{6}{7},\frac{2}{7},\frac{3}{7}$

$\therefore$ Equation of line $PQ\Rightarrow \frac{x+2}{\frac{6}{7}}=\frac{y-1}{\frac{2}{7}}=\frac{z+8}{\frac{3}{7}}$

$\therefore$ Let $P$ be $(\frac{6}{7}r-2,\frac{2}{7}r+1,\frac{3}{7}r-8)$

$\therefore {(\frac{6}{7}r-2+2)}^2+{(\frac{2}{7}r+1-1)}^2+{(\frac{3}{7}r-8+8)}^2={21}^2={PQ}^2\frac{(36+4+9)}{49}{r}^2={21}^2\Rightarrow r=21,-21$

$\therefore$ Co-ordinates of $P$ can be $(16,7,1)$ & $(-20,-5,-17)$