If $α, β, γ$ are the angles which a line makes with the positive directions of coordinate axes, then ${sin}^{2} α + {sin}^{2} β + {sin}^{2} γ$ is equal to

$(a) 0 (b) 1$
$(c) 2 (d) 3$

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Solution

$cos α, cos β, cos γ$ are the direction cosines of the line.
$\Rightarrow {cos}^{2} α + {cos}^{2} β + {cos}^{2} γ = 1$
$\Rightarrow (1 - {sin}^{2} α) + (1 - {sin}^{2} β) + (1 - {sin}^{2} γ) = 1$
$\Rightarrow {sin}^{2} α + {sin}^{2} β + {sin}^{2} γ = 2$

Option $(c)$ is correct.

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