- #1
dr721
- 23
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Homework Statement
So I have several problems on my homework which deal with the application of cross product and its magnitude to find areas. I know how to do cross product, and I know how to find the magnitude, however, no matter how many times I try to calculate it, I get the wrong answer.
Take for example:
Find the area of the triangle with the three vertices [0, 0, -5], [-2, 1, -4], and [-3, -1, -6].
2. The attempt at a solution
This is where I'm not sure if I'm doing something incorrectly. I have generally been trying to create the two vectors for the cross product by subtracting one vertex from the other two.
So,
[-2, 1, -4] - [0, 0, -5] = [-2, 1, 1]
and
[-3, -1, -6] - [0, 0, -5] = [-3, -1, -1]
Then, computing the cross product to be [0, 5, 5]
So the magnitude comes out to be [itex]\sqrt{50}[/itex]
And then the area of the triangle would be [itex]\frac{1}{2}[/itex][itex]\sqrt{50}[/itex]
Is this right? If not, where did I go wrong? Is there some proper approach to deciding which vertex to use as the starting point?
Thanks for your help.