- #1

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I'm trying to understand how this formula: 1/2 magnitude of v × w (area of triangle)

yields the same value no matter which 2 adjacent sides are chosen.

How would you prove mathematically that this is the case?

- Thread starter Neen87
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- #1

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I'm trying to understand how this formula: 1/2 magnitude of v × w (area of triangle)

yields the same value no matter which 2 adjacent sides are chosen.

How would you prove mathematically that this is the case?

- #2

tiny-tim

Science Advisor

Homework Helper

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Hi Neen87! Welcome to PF!

Hint: call the vertices

- #3

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Because if you draw the parallelogram with sides

I'm trying to understand how this formula: 1/2 magnitude of v × w (area of triangle)

yields the same value no matter which 2 adjacent sides are chosen.

How would you prove mathematically that this is the case?

[tex]|v \times w| = |v||w|\sin\theta[/tex]

where [itex]\theta[/itex] is the angle between the two vectors you have chosen for sides. Now, whichever two sides you choose and whichever direction they point, the angle between them will be either [itex]\theta[/itex] or [itex]\pi - \theta[/itex]. Either way you get the same value for its sine.

- #4

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Thanks so much! :-)

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