If a vector $\to A$ makes an angles $α, β$ and $Y$ respectively with the $x$ , $y$ and $z$ axes respectively. Then ${sin}^{2} α + {sin}^{2} β$ $+ s i n^{2} γ$ is equal to

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Solution

The correct option is C $2$
By the definition of direction cosines,

${cos}^{2} α + {cos}^{2} β + {cos}^{2} γ = 1$

$1 - {sin}^{2} α + 1 - {sin}^{2} β + 1 - {sin}^{2} γ = 1$

${sin}^{2} α + {sin}^{2} β + {sin}^{2} γ = 3 - 1 = 2$

Option $C$ is the correct answer

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