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I'm doing problems which have me calculate the volumes of parallelpipeds I'm slightly confused with this. I know the formula is:

[tex]V=\vec{a} \cdot (\vec{b}\times\vec{c})[/tex]

where a and b form the base, with c being the "vertical" side. My issue is that when given three vectors which define this shape, how do I know which order to put the vectors in? For one example I was given the vectors:

<6,3,-1>

<0,1,2>

<4,-2,5>

and after drawing them out I had no clue which was which, so I just decided to use them in order as a, b, and c. It worked.

Then in the next problem I was given four points:

P(2,0,-1)

Q(4,1,0)

R(3,-1,1)

S(2,-2,2)

And told that three sides were defined by PQ, PR, and PS. So after getting those vectors I again just took them in order and got -3. The correct answer is three.

How do I determine which vectors I put in which place in the equation? In the examples they just pick three in order and use them that way.

[tex]V=\vec{a} \cdot (\vec{b}\times\vec{c})[/tex]

where a and b form the base, with c being the "vertical" side. My issue is that when given three vectors which define this shape, how do I know which order to put the vectors in? For one example I was given the vectors:

<6,3,-1>

<0,1,2>

<4,-2,5>

and after drawing them out I had no clue which was which, so I just decided to use them in order as a, b, and c. It worked.

Then in the next problem I was given four points:

P(2,0,-1)

Q(4,1,0)

R(3,-1,1)

S(2,-2,2)

And told that three sides were defined by PQ, PR, and PS. So after getting those vectors I again just took them in order and got -3. The correct answer is three.

How do I determine which vectors I put in which place in the equation? In the examples they just pick three in order and use them that way.

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