First slide

Direction ratios and direction cosines

Question

If $P (- 2, - 4, - 9)$ and direction cosines of $\vec{O P}$ are $(α, β, γ)$ , then $(α + β + γ) \times \sqrt{101}$ is

Easy

A

101
B

72
C

-15
D

None

Solution

The direction cosines of the line $\vec{O P}$ are $〈- \frac{2}{\sqrt{4 + 16 + 81}}, - \frac{4}{\sqrt{4 + 16 + 81}}, - \frac{9}{\sqrt{4 + 16 + 81}}〉$
Consider
Therefore, the required value is $\begin{matrix} (α + β + γ) \times \sqrt{101} = \frac{- 2 - 4 - 9}{\sqrt{101}} \times \sqrt{101} \\ = - 15 \end{matrix}$
Therefore, the required value is $- 15$

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