Chapter 8.7, Problem 37PPS

To determine

To calculation:

Vector in component form.

Answer to Problem 37PPS

The vector in component form is $\langle -1.7,6.8\rangle$ .

Explanation of Solution

Given information:

Magnitude = $7$

Direction = ${104}^{\circ }$ .

Calculation:

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

  $\begin{array}{l}\cos {104}^{\circ }=\frac{x}{7}\\ x=7\cos {104}^{\circ }\approx -1.69\\ \sin {104}^{\circ }=\frac{y}{7}\\ y=7\sin {104}^{\circ }\approx 6.79\end{array}$

As the direction indicates the vector in quadrant one so, the solution is $\langle -1.7,6.8\rangle$ .