Question

If three vectors A B and C have magnitudes of 5 12 and 13 and A+B=C then what is the cosine of the angle between B and C

Answer 1

Explanation: Given that A + B = C, we can use the law of cosines to find the cosine of the angle between B and C. The law of cosines states that for any triangle with sides a, b, and c, and an angle C opposite side c:

cos(C) = (a^2 + b^2 - c^2) / 2ab

In this case, we are given that A + B = C, so we can substitute C = A + B into the law of cosines to get:

cos((A + B)) = (A^2 + B^2 - (A + B)^2) / 2AB

Expanding the right side of this equation, we get:

cos((A + B)) = (A^2 + B^2 - A^2 - 2AB - B^2) / 2AB

Canceling out like terms, we are left with:

cos((A + B)) = -2AB / 2AB

Simplifying, we get:

cos((A + B)) = -1

Therefore, the cosine of the angle between B and C is -1.