# Thread: Vectors - parallelepiped volume

1. ## Vectors - parallelepiped volume

I think this is a parallelogram prism?

This is the components given:

vectors:

a=(2, -5, -1)
b=(3,0,1)
c=(3,-1,-1)

So, I thought if this was a parallel prism, find a cross-product b, get the magnitude (area of parallelogram) and then multiply by magnitude of the third vector (depth?). But I get the wrong answer. I'm getting 71, the answer is 29. Any help?

2. Originally Posted by theowne
I think this is a parallelogram prism?

This is the components given:

vectors:

a=(2, -5, -1)
b=(3,0,1)
c=(3,-1,-1)

So, I thought if this was a parallel prism, find a cross-product b, get the magnitude (area of parallelogram) and then multiply by magnitude of the third vector (depth?). But I get the wrong answer. I'm getting 71, the answer is 29. Any help?
i keep getting 25. are you sure you typed the vectors correctly?

3. You're right, I typed wrong, the correct vector for b is (4,0,1). Er, can you tell me what steps you took?

4. Just take the determinant of your vectors. You will get -29. Of course, we need the absolute value.

5. Originally Posted by theowne
You're right, I typed wrong, the correct vector for b is (4,0,1). Er, can you tell me what steps you took?
i did what galactus suggested.

the volume is given by $V = \left| \begin{array}{ccc} 4 & 0 & 1 \\ 2 & -5 & - 1 \\ 3 & - 1 & -1 \end{array}\right|$ .........of course i mean the determinant of that matrix

and also as galactus said, if you get a negative answer, just take the absolute value

6. Also, $a\cdot{(b\times{c})}$ will give you the same thing.

Take the cross product of b and c. Then dot product that with a.

7. But how does that relate with the question? How are those equations related to finding the volume of a parallelepiped, what does each part represent? Why are you doing bxc dot product with a? To start, am I right that this is a parallelogram prism?

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### parallopipe

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