Physics

Problem

From the origin

O

, two displacement vectors are drawn:

\mathbf{A}

has magnitude

12\,\text{m}

and makes an angle of

135^{\circ}

with the positive

x

-axis;

\mathbf{B}

has magnitude

15\,\text{m}

and makes an angle of

-45^{\circ}

with the positive

x

-axis (i.e.,

45^{\circ}

below it). a. (i) Express

\mathbf{A}

and

\mathbf{B}

individually in unit-vector notation. b. (ii) Obtain the resultant displacement

\mathbf{R}=\mathbf{A}+\mathbf{B}

in unit-vector form. c. (iii) Calculate the magnitude of

\mathbf{R}

and the angle it makes with the positive

x

-axis, quoting the angle to the nearest degree.