Find the component form of v given its magnitude and the angle it makes with the positive x-axis. $\begin{array}{lr}\text { Magnitude}&\text { Angle }\\|\mathbf{v}\|=4&0^o
\end{array}$

A) $\langle 0,0 \rangle$
B) $\langle 4,4 \rangle$
C) $\langle 0,4 \rangle$
D) $\langle 4,0 \rangle$
E) $\langle - 4,0 \rangle$

Question

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. $\begin{array}{lr}\text { Magnitude}&\text { Angle }\\|\mathbf{v}\|=4&0^o
\end{array}$

A) $\langle 0,0 \rangle$
B)  $\langle 4,4 \rangle$
C)  $\langle 0,4 \rangle$
D)  $\langle 4,0 \rangle$
E)  $\langle - 4,0 \rangle$

Quizplus · Accepted Answer

The component form of a vector given its magnitude $r$ and angle $\theta$ with the positive x-axis can be found using the formulas $x = r\cos(\theta)$ and $y = r\sin(\theta)$. For a magnitude of 4 and an angle of $0^o$, the x-component is $4\cos(0^o) = 4$ and the y-component is $4\sin(0^o) = 0$, making the component form $\langle 4,0 \rangle$.

Find the Component Form of V Given Its Magnitude and the Angle