Given a vector $q$ with length 3 and direction angle $32^{\circ}$, write $q$ in component form.

Step 1 ：We are given a vector $q$ with length 3 and direction angle $32^{\circ}$. We are asked to write $q$ in component form.

Step 2 ：The component form of a vector is given by $q = |q|(\cos \theta, \sin \theta)$, where $|q|$ is the magnitude of the vector and $\theta$ is the direction angle.

Step 3 ：In this case, $|q| = 3$ and $\theta = 32^{\circ}$. However, trigonometric functions use radians, not degrees, so we need to convert the angle from degrees to radians. The conversion gives us $\theta = 0.5585053606381855$ radians.

Step 4 ：We can now calculate the x and y components of the vector. The x component is $|q| \cos \theta = 3 \cos 0.5585053606381855 = 2.544144288469278$ and the y component is $|q| \sin \theta = 3 \sin 0.5585053606381855 = 1.5897577926996147$.

Step 5 ：These values represent the vector in component form. Therefore, the vector $q$ in component form is \(\boxed{(2.54, 1.59)}\).