Chapter 8.7, Problem 36PPS

To determine

To calculation:

Vector in component form.

Answer to Problem 36PPS

The vector in component form is $\langle -11.6,-3.1\rangle$ .

Explanation of Solution

Given information:

Magnitude = $12$

Direction = ${195}^{\circ }$ .

Calculation:

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

  $\begin{array}{l}\cos {195}^{\circ }=\frac{x}{12}\\ x=12\cos {195}^{\circ }\approx -11.59\\ \sin {195}^{\circ }=\frac{y}{112}\\ y=12\sin {195}^{\circ }\approx -3.11\end{array}$

As the direction indicates the vector in quadrant one so, the solution is $\langle -11.6,-3.1\rangle$ .