the vector $vec{u}$ is shown below. find the component form of $vec{u}$. round your final answers to the…

Explanation:

Step1: Recall component - form formula

For a vector $\vec{u}$ with magnitude $r$ and direction angle $\theta$, the component - form is given by $\vec{u}=(r\cos\theta,r\sin\theta)$. Here, $r = 6$ and $\theta=335^{\circ}$.

Step2: Calculate the $x$ - component

$x = r\cos\theta=6\cos(335^{\circ})$. Since $\cos(335^{\circ})=\cos(360^{\circ}- 25^{\circ})=\cos(25^{\circ})\approx0.9063$, then $x = 6\times0.9063 = 5.44$.

Step3: Calculate the $y$ - component

$y = r\sin\theta=6\sin(335^{\circ})$. Since $\sin(335^{\circ})=\sin(360^{\circ}-25^{\circ})=-\sin(25^{\circ})\approx - 0.4226$, then $y=6\times(-0.4226)=-2.54$.

Answer:

$(5.44,-2.54)$