Asked by Melinda
Do the vectors (2,0,1),(-2,0,0) and (2,3,0) lie on the same plane? Explain your reasoning.
Answers
Answered by
Steve
take the triple product
(2,0,1)•(-2,0,0)×(2,3,0)
| 2 0 1 |
|-2 0 0 | = -6
| 2 3 0 |
so the vectors are not coplanar.
The product represents the volume of the parallelopiped with the three vectors as edges. If they are coplanar, the volume is zero.
(2,0,1)•(-2,0,0)×(2,3,0)
| 2 0 1 |
|-2 0 0 | = -6
| 2 3 0 |
so the vectors are not coplanar.
The product represents the volume of the parallelopiped with the three vectors as edges. If they are coplanar, the volume is zero.
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