Answer
$\langle 10, 10\sqrt 3 \rangle$ or $10 i + 10\sqrt 3 j$
Work Step by Step
Step 1. Identity the given quantities: length of the vector $|\vec u|=20$, angle $\theta=60^{\circ}$ 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: $u_x=|\vec u|cos\theta=20cos60^{\circ}=10$ and $u_y=|\vec u|sin\theta=20sin60^{\circ}=10\sqrt 3$
Step 4. Write the vector in its component forms $\vec u=\langle 10, 10\sqrt 3 \rangle=10 i + 10\sqrt 3 j$
