(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Ok so my book says that the volume of a parallelepiped is:

V= |b cross c||a||cos(theta)| = |a dot (b cross c)|, where a, b, and c are vectors

I get the "|b cross c||a||cos(theta)|" part because I can see the geometry but I don't get how they get from that to |a dot (b cross c)|.

2. Relevant equations

3. The attempt at a solution

I see how |a||cos(theta)| looks kinda familiar so I tried to figure out using that.

So I know a dot b = |a||b|cos(theta), so

|a|cos(theta) = (a dot b)/|b| but then if I plug that quantity in it doesn't seem to work.

So can anyone help me see why |b cross c||a||cos(theta)| = |a dot (b cross c)| ?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Please explain volume of parallelepiped

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