Question

Find the direction cosines and direction ratios of the line joining the points
$A(1,3,5),B(-1,0,-1)$

Answer 1

Given the points $A\left(1,3,5\right)\&B\left(-1,0,-1\right)$

Direction ratios are $a=-1-1=-2b=0-3=-3c=-1-5=-6,$

Now, $\sqrt{a^2+b^2+c^2}=\sqrt{{\left(-2\right)}^2+{\left(-3\right)}^2+{\left(-6\right)}^2}=\sqrt{4+9=36}=\sqrt{49}=7$

Direction cosines are

$l=\frac{a}{\sqrt{a^2+b^2+c^2}}=\frac{-2}{7}m=\frac{b}{\sqrt{a^2+b^2+c^2}}=\frac{-3}{7}n=\frac{c}{\sqrt{a^2+b^2+c^2}}=\frac{-6}{7}$.