Two vectors and each have magnitude

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Two vectors

\vec{a}

and

\vec{b}

each have magnitude

p

. Without calculation, describe how the magnitude of

\vec{a}+\vec{b}

varies as the angle between the two vectors increases from

0^{\circ}

180^{\circ}

and give a brief reason.