If - - - be the angles which a line makes with the positive direction of co-ordinate axes- then sin2- - sin2- - sin2- -RPET 2000- AMU 2002- MP PET 1989- 98- 2000- 03- Pb- CET 2001-

Since cos^2 α + cos^2 β + cos^2 γ = 1 ⇒ ∑ sin^2 α = 3 1 = 2. ...

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Standard XII

Mathematics

Coordinate Axes in Three Dimensional Space

If α, β, γ be...

Question

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]

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Solution

The correct option is A
2

Since $c o s^{2} α + c o s^{2} β + c o s^{2} γ = 1 \Rightarrow \sum s i n^{2} α = 3 - 1 = 2.$

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If α,β,γ be the angles which a line makes with the positive direction of co-ordinate axes, then sin2α+sin2β+sin2γ= [RPET 2000; AMU 2002; MP PET 1989, 98, 2000, 03, Pb. CET 2001]

The correct option is A 2 Since cos2 α+cos2 β+cos2 γ=1 ⇒ ∑ sin2 α=3−1=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]

The correct option is A
2

Since $c o s^{2} α + c o s^{2} β + c o s^{2} γ = 1 \Rightarrow \sum s i n^{2} α = 3 - 1 = 2.$