Question

Suppose two initial vectors intersect at a right angle and form a resultant vector. The magnitudes of one initial vector, A, and the resultant vector, R, are given.

Which formula can be used to find the magnitude of the other initial vector, B?

B2 = A2 - R2
B2 = R2 + A2
B2 = A + R
B2 = R2 - A2

Answer 1

Since A and B are perpendicular, R is the hypotenuse of a right triangle: R^2 = A^2 + B^2. Solving for B^2 gives

B^2 = R^2 − A^2.