Question

Vectors tetrahedron and parallelopiped scalar triple product

Answer 1

Answer:

Step-by-step explanation:

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Here is one way to think of it. A tetrahedron is 16 of the volume of the parallelipiped formed by a⃗ ,b⃗ ,c⃗ . The volume of the parallelepiped is the scalar triple product |(a×b)⋅c|. Thus, the volume of a tetrahedron is 16|(a×b)⋅c|

In order to solve the question like you are trying to, notice that by V=13Bh=16||a×b||⋅h. Then, h=||c||⋅|cos(θ)|. Thus, we have V=16||a×b||⋅||c||⋅|cos(θ)|. Now see that |c⋅(a×b)|=||c||⋅||(a×b)||⋅|cos(θ)| and thus V=16|(a×b)⋅c|.

I'd also like to say that the notation you are using is a little weird. In order to avoid confusion, |x| denotes absolute value and ||x|| denotes magnitude.

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edited Jul 17 '16 at 1:12

answered Jan 7 '16 at 21:02

if I wanted to arrive at the given equation from my previous answer of 12|a×b|×|c|cosθ, is it possible?

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