Answer
$\langle 7.74, 11.06 \rangle$ or $ 7.74i+ 11.06 j$
Work Step by Step
Step 1. Identity the given quantities: length of the vector $|\vec u|=13.5$, angle $\theta=125^{\circ}$ with respect to the $+x$-axis.
Step 2. Recall the general component form of a vector $\vec u=\langle u_x, u_y \rangle=u_x i + u_y j$ where $u_x, u_y$ are the components of the vector along the horizontal and vertical axes.
Step 3. Calculate the components as: $u_x=|\vec u|cos\theta=13.5cos125^{\circ}\approx7.74$ and $u_y=|\vec u|sin\theta=13.5sin125^{\circ}\approx11.06$
Step 4. Write the vector in its component forms $\vec u=\langle 7.74, 11.06 \rangle= 7.74i+ 11.06 j$
