QuestionFind the unit vector that has the same direction as the vector $\mathbf{v}$. $$\mathbf{v}=8 \mathrm{j}$$
The unit vector that has the same direction as the vector $\mathbf{v}$ is $\square$ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Type your answer in the form ai + bj.)

Studdy Solution
Divide the vector $\mathbf{v}$ by its magnitude to find the unit vector.
The unit vector $\mathbf{u}$ in the direction of $\mathbf{v}$ is given by:
$$\mathbf{u} = \frac{\mathbf{v}}{\|\mathbf{v}\|}$$
Substitute $\mathbf{v} = 8\mathbf{j}$ and $\|\mathbf{v}\| = 8$:
$$\mathbf{u} = \frac{8\mathbf{j}}{8} = \mathbf{j}$$
The unit vector that has the same direction as the vector $\mathbf{v}$ is:
$$\boxed{\mathbf{j}}$$