Two vectors act at a point

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

Two vectors act at a point. Vector

\mathbf{A}

has magnitude

7\,\text{units}

and acts at

25^{\circ}

above the positive x-axis. Vector

\mathbf{B}

has magnitude

10\,\text{units}

and acts along the negative y-axis. (i) Represent

\mathbf{A}

and

\mathbf{B}

to scale on graph paper, placing the tail of

\mathbf{B}

at the head of

\mathbf{A}

. Measure the magnitude and direction of the resultant vector. (ii) Resolve

\mathbf{A}

and

\mathbf{B}

into rectangular components, add the components algebraically, and hence calculate exactly the magnitude and direction of the resultant.