10.4: Problem 9 (updated)

Dr.Taylor
In class we talked about finding the volume of a paralelipiped for a couple minutes and I tried to find the scalar triple product but the answer I got was wrong and I don't know if it has to do with the ordering of the vectors or if it doesn't matter. Thank you for any help you can give.

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Well, it's hard to help without doing the problem for you, because you didn't tell me what you did, your didn't tell me what you tried to do, not to mention also that you didn't actually ask a question. However, taking a stab in the dark, you might want to pay attention to the fact that the scalar triple product is the scalar triple product, while you have four points. What do you make of that?

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I read the blog post and I realize where I went wrong with my wording. I'm taking the scalar triple product of the 3 vectors PQ, PR, and PS in that order. I've tried using different orders as well but none of them seem to work. I wanted to know if the order of the vectors matters and if it does, how do I know which order to put them in.
Sincerely,
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Ok, got it. It sounds like you mostly know what you're doing.  The order matters only in the sign of the determinant.  And since you're taking the absolute value of the scalar triple product in order to get a positive number for the volume,  remember, the order doesn't affect your answer at all.  So...a few thoughts:
1) if, as it sounds like, you're getting different answers for different orders you're doing one of the operations wrong, either the dot product or the cross product but you might also have made a mistake in computing the three vectors PQ, PR and PS.
2) the true answer is smaller than either of the two answers I've seen you try.
3) there are a lot of minus signs in those vectors, a common source of arithmetic mistakes is forgetting that two minuses is a plus. I'd guess that the mistake is most likely in the cross product (but I wouldn't bet even money on it).

PS: if you wrote up your computations LEGIBLY you could take a photo with your phone and email it to me