If $α, β, γ$ , yare angle which is directed line makes with the positive direction of the co-ordinate axes, then ${sin}^{2} α + {sin}^{2} β + {sin}^{2} γ$

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{2}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $2$
Since, $α$ , $β$ and $γ$ be the angle made by the line with co-ordinate axes.
Therefore, ${cos}^{2} α + {cos}^{2} β + {cos}^{2} γ = 1$
$\Rightarrow 1 - {sin}^{2} α + 1 - {sin}^{2} β + 1 - {sin}^{2} γ = 1$
$\Rightarrow {sin}^{2} α + {sin}^{2} β + {sin}^{2} γ = 2$
Ans: D

Suggest Corrections

Similar questions

Q. If a line makes angles

α, β, γ

with positive direction co-ordinate axes then prove that

{sin}^{2} α + {sin}^{2} β + {sin}^{2} γ = 2

If $α, β, γ$ be the angles which a line makes with the positive direction of co-ordinate axes, then $s i n^{2} α + s i n^{2} β + s i n^{2} γ =$
[RPET 2000; AMU 2002; MP PET 1989, 98, 2000, 03, Pb. CET 2001]

Q. If a line angles α, β, γ with positive directions of the coordinate axes, then the value of sin²α + sin²β + sin² γ is __________.

Q. If

α, β

and

γ

are the angles which a half ray makes with the positive direction of the axes, then

{sin}^{2} α + {sin}^{2} β + {sin}^{2} γ

is equal to

Q. A line makes an angle

α, β, γ

with the

X, Y, Z

axes. Then

{sin}^{2} α + {sin}^{2} β + {sin}^{2} γ =

Join BYJU'S Learning Program

If α,β,γ, yare angle which is directed line makes with the positive direction of the co-ordinate axes, then sin2α+sin2β+sin2γ

The correct option is D 2Since, α, β and γ be the angle made by the line with co-ordinate axes.Therefore, cos2α+cos2β+cos2γ=1⇒1−sin2α+1−sin2β+1−sin2γ=1⇒sin2α+sin2β+sin2γ=2Ans: D

If $α, β, γ$ , yare angle which is directed line makes with the positive direction of the co-ordinate axes, then ${sin}^{2} α + {sin}^{2} β + {sin}^{2} γ$