1. perhaps this should go in the maths section, but since i read it out of a physics book i'll put it here.

i read in a physics book one day you see and came across an equation for addition of vectors basically saying, when vectors A and B are added the resultant vector is equal to:

R<sup>2</sup>=A<sup>2</sup>+B<sup>2</sup>+2(A)(B)(COS a)

the first part i can see as being pythagorus and only applying to addition at right angles, so by logical deduction the second part is for addition at non-right angles.

can someone explain why we add 2(A)(B)(COS a) to obtain the answer?  2.

3. Thats a binom, with ab cos(ab) as the scalar product.  4. why do we add the scalar product and the vector magnitude?  5. This is known as the "law of cosines" in trigonometry. And yes it is a generalization of the pythagorean theorem to triangles which are not right triangles. Caution, however, a in your formula is not the angle opposite side A, but the angle opposite side R of the triangle. Ultrashotgun is pointing out that it can be derived from vector math.

Given that R is the vector sum of two vectors A and B, R = A+B, then the magnitude of R is the square root of the dot product of R with itself, or in other words,
R^2 = R dot R = (A+B) dot (A+B)
where R is the magnitude of the vector R then by the distributive property we havt that
R^2 = A dot A + A dot B + B dot A + B dot B
but A dot A is just A^2 the square of the magnitude of A, likewise, B dot B is B^2.
and A dot B = B dot A = A*B*cos(angle between vectors A and B)
where A and B are the magnitudes of vectors A and B.

So we have
R^2 = A^2 + B^2 + 2*A*B*cos(angle between vectors A and B)  6. thank you all.

thats cleared up a lot of confusion for me.  Bookmarks
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