Physics

Problem

A displacement vector

\mathbf{R}

is resolved into rectangular components

R_x

and

R_y

along the

x

- and

y

-axes respectively. a. (i) Using a neatly labelled right-angled triangle, explain why the magnitude of

\mathbf{R}

depends only on

R_x

and

R_y

. State the relationship obtained. b. (ii) Describe, with reasoning, how the direction of

\mathbf{R}

with respect to the positive

x

-axis can be expressed in terms of

R_x

and

R_y

for vectors situated in all four quadrants.