I want to prove | r → − s → | 3 = ( r...

stratsticks57jl

stratsticks57jl

Answered

2022-07-20

I want to prove
| r s | 3 = ( r 2 + s 2 2 r s cos ( θ ) ) 3 / 2
where r = | r | . but I have problems because
( r 2 + s 2 2 r s cos ( θ ) ) 3 / 2 = ( r 2 + s 2 r s ) 3 / 2 = ( ( r s ) 2 ) 3 / 2 = ( r s ) 3
I hope someone can help me.

Answer & Explanation

bardalhg

bardalhg

Expert

2022-07-21Added 15 answers

This is a standard derivation. Start with the fact that | v | 2 = v v applied to v = r s to get
| r s | 2 = ( r s ) ( r s ) .
Now expand the dot product to get
| r s | 2 = r 2 + s 2 2 r s = r 2 + s 2 2 r s cos ( θ ) .
Now take the square root of both sides, then cube. Done.

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