Mathematics

Problem

Two vectors

\mathbf A

and

\mathbf B

have magnitudes

A

and

B

and include an angle

\theta

between them. a. Resolve

\mathbf A

and

\mathbf B

into rectangular components along mutually perpendicular axes. b. Add the components to obtain the resultant vector

\mathbf R

in component form. c. Hence, derive an expression for the magnitude

R

of the resultant in terms of

A

B

, and

\theta

. d. Show that your expression reduces to the Pythagorean theorem when the two vectors are perpendicular.