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Please help find the volume of the parallelepiped with adjacent edges are vector PQ, vector PR and vector PS where?
P=(1,1,1)
Q=(2,0,3)
R=(4,1,7)
S=(3,-1,-2)
2 Answers
- PinkgreenLv 73 years ago
The volume is
|v|=the absolute value of
|..1..-1..2..|
|..3...0..6..|
|..2..-2.-3..|
=the absolute value of
|..1..-1..2..|
|..3...0..6..|
|..0...0.-7..|
=21
- husoskiLv 73 years ago
The volume is the absolute value of the triple product:
V = | (Q-P) • [(R-P) × (S-P)] |
= | <1, -1, 2> • [<3, 0, 6> × <2, -2, -3>] |
You can grind out the cross- and dot-products, or treat that is a single "triple product" operator, equivalent to the determinant:
| 1 .-1 . 2 |
| 3 . 0 . 6 |
| 2 .-2 .-3 |
Either way, you should get 21 as the answer.
