First slide

Direction ratios and direction cosines

Question

$P (0, 4, - 1), Q (- 1, 2, - 3) and R (5, 0, - 6)$ are the vertices of a triangle. The direction ratios of the internal angular bisector of $∠ P Q R$ are

Moderate

A

$(25, 18, 5)$
B

$(25, 8, 5)$
C

$(25, 8, 15)$
D

None

Solution

Given $P (0, 4, - 1), Q (- 1, 2, - 3) a n d R (5, 0, - 6)$ .
Now $\vec{Q P} = (1, 2, 2) a n d \vec{Q R} = (6, - 2 - 3)$ .
The angle bisector of $∠ P Q R$ is $\pm (\frac{\vec{Q P}}{|\vec{Q P}|} + \frac{\vec{Q R}}{|\vec{Q R}|}) = \pm (\frac{25}{21}, \frac{8}{21}, \frac{5}{21})$
$\Rightarrow (25, 8, 5) a r e d . r' s o f t h e a n g u l a r b i s e c t o r o f ∠ P Q R$

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