A geometry problem by Krishna Ar
A vector P makes angles α , β , γ with the three co-ordinate axes respectively. Then the value of sin 2 α + sin 2 β + sin 2 γ ?
Note: The vector is in a 3-d plane.
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2 solutions
I just made a guess. This happens in a right angled triangle... :-P
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Oh really -_-
Or just s i n 2 α + c o s 2 α + s i n 2 9 0
c o s 2 α + c o s 2 β + c o s 2 γ = 1 s o a n s w e r i s 2 .
how do you do this??
Can you add an explanation of where you obtained the first equality from?
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It is a basic identity in Vector Algebra.
Why is this problem flagged?
Yeah, why is this flagged?
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The report stated "You should clarify that this is a vector in 3-D, instead of a vector in higher dimensions."
I agree with this, and see that the problem has been updated.
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@Calvin Lin – That's alright. Thanks. I felt that it was self-understood though
sir i want to ask what is the sum of three angles that a 3-d vector makes
with all 3 axes ??
sin 2 α + sin 2 β + sin 2 γ = ( 1 − cos 2 α ) + ( 1 − cos 2 β ) + ( 1 − cos 2 γ ) = 1 + 1 + 1 − ( cos 2 α + cos 2 β + cos 2 γ ) = 3 − 1 = 2