Triangle Inequality and the Triangle Law of Vector Addition

  • Thread starter Ryuzaki
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  • #1

Main Question or Discussion Point

The triangle inequality states that, the sum of any two sides of a triangle must be greater than the third side of the triangle.

But the triangle law of vector addition states that if we can represent two vectors as the two sides of a triangle in one order ,the third side of the triangle taken in the reverse order will be the sum of the two vectors.

However, the above two laws seem to contradict each other; one states that the third side should be less than the sum of the other two sides, while the other law states that it would be equal (considering the magnitudes of the vectors).

So can anyone tell me what I'm missing here? Thanks.

Answers and Replies

  • #2
Hi Ryuzaki
The third vector is the sum of the two first vectors, but its length is not the sum of the lengths of the vectors.
  • #3
Science Advisor
The length of the third vector can be calculated using the law of cosines.
  • #4
Thank you, oli4 and mathman. Seems like I had a pretty silly misconception there.