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## Homework Statement

Three vectors, [itex]\vec A, \vec B, \vec C[/itex] originiate from a common point, and have their heads in a plane.

Show that [itex]\vec A \times \vec B + \vec B \times \vec C + \vec C \times \vec A[/itex] is perpendicular to the plane.

## Homework Equations

I'm not exactly sure, but probably solvable with the definition of a cross product (or even without it?)

## The Attempt at a Solution

First, I attempted to simplify the problem by assuming all three vectors were in the same plane, and that they all pointed to a line (simplified version of a plane). However, it turned out that the sum of the three cross products seem to be

*parallel*, not perpendicular to the plane/line.

Then, I tried solving the problem using the mathematical definition of cross products, after assigning angles between each pair of vectors. However I'm not sure how to relate the three.

I'm guessing this may need to be solved by breaking the vectors down into components, or there is a much simpler method that I'm just not seeing.. I'd really appreciate it if someone can give me a hint or point me in the right direction! :)