Answer
True
Work Step by Step
Using question 85 if two vectors have the same magnitude and direction then they must be equivalent. We must find the magnitude and direction of $\mathbf{v}$ and $\|\mathbf{v}\|\mathbf{u}$. By definition the magnitude of $\mathbf{v}$ is $\|\mathbf{v}\|$. Magnitude of $\|\mathbf{v}\|\mathbf{u}$=$\|\mathbf{v}\|\|\mathbf{u}\|$ Since $\mathbf{u}$ is a unit vector, $\|\mathbf{v}\|\|\mathbf{u}\|$=$\|\mathbf{v}\|\times1=\|\mathbf{v}\|$. Next, since $\mathbf{u}$ is in the same direction as $\mathbf{v}$, and scalar multiplication doesn't impact direction, then $\|\mathbf{v}\|\mathbf{u}$ has the same direction as $\mathbf{v}$.
