$If α, β, γ$ 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

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Solution

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

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[RPET 2000; AMU 2002; MP PET 1989, 98, 2000, 03, Pb. CET 2001]

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If α,β,γ are the angles which a line makes with the positive directions of coordinate axes, then sin2α+sin2β+sin2γ is equal to

The correct option is B 2 cosα,cosβ,cosγ are the direction cosines of the line. ⇒cos2α+cos2β+cos2γ=1 ⇒(1−sin2α)+(1−sin2β)+(1−sin2γ)=1 ⇒sin2α+sin2β+sin2γ=2

$If α, β, γ$ 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

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