Chapter 8.7, Problem 35PPS

To determine

To calculation:

Vector in component form.

Answer to Problem 35PPS

The vector in component form is $\langle 4.0,3.0\rangle$ .

Explanation of Solution

Given information:

Magnitude = $5$

Direction = ${37}^{\circ }$ .

Calculation:

Magnitude is the hypotenuse measurement. Use cosine to get the $x$ component and sine to get $y$ component.

  $\begin{array}{l}\cos {37}^{\circ }=\frac{x}{5}\\ x=5\cos {37}^{\circ }\approx 3.99\\ \sin {37}^{\circ }=\frac{y}{5}\\ y=5\sin {37}^{\circ }\approx 3.01\end{array}$

The solution is

  $\begin{array}{l}\overrightarrow{v_1}=\langle -4,-3\rangle \\ \overrightarrow{v_2}=\langle 4.0,3.0\rangle \end{array}$

As the direction indicates the vector in quadrant one so, the solution is $\langle 4.0,3.0\rangle$ .