Question

Find the direction cosines and direction ratios of the line joining the points
$A(0,0,0,),B(4,8,-8)$

Answer 1

Given the points $A\left(0,0,0\right)\&B\left(4,8,-8\right)$

Direction ratios are $a=4-0=4b=8-0=8c=-8-0=-8$

Now, $\sqrt{a^2+b^2+c^2}=\sqrt{4^2+8^2+8^2}=\sqrt{16+64+64}=\sqrt{144}=12$

Direction cosines are

$l=\frac{a}{\sqrt{a^2+b^2+c^2}}=\frac{4}{12}=\frac{1}{3}m=\frac{b}{\sqrt{a^2+b^2+c^2}}=\frac{8}{12}=\frac{2}{3}n=\frac{c}{\sqrt{a^2+b^2+c^2}}=\frac{-8}{12}=-\frac{2}{3}$