Find the direction cosines and direction ratios of the line joining the points
$A (4, 2, - 6), B (- 2, 1, 3)$

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Solution

$\begin{matrix} d i r e c t i o n r a t i o o f l i n e A B = (- 2, 0), (1 - 2), (3 + 6) = - 6, - 1, 9 \Rightarrow a n d d i r e c t i o n c o s i n e i s \frac{- 6}{\sqrt{{(- 6)}^{2} + {(- 1)}^{2} + 9^{2}}}, \frac{1}{\sqrt{{(- 6)}^{2} + {(- 1)}^{2} + 9^{2}}}, \frac{9}{\sqrt{{(- 6)}^{2} + {(- 1)}^{2} + 9^{2}}} \frac{- 6}{\sqrt{118}}, \frac{- 1}{\sqrt{118}}, \frac{9}{\sqrt{118}} A n s . \end{matrix}$

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