Two vectors ( A ) and ( B ) have magnitudes (A ) and (B ) and include an angle ( )…

MATHEMATICS · Multi-part · A Level · Mathematics · Vectors · Vectors

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.