The correct answer is True but I don't understand how this is.
How about a vector of value 2? This is a non-zero vector. How can this be parallel to a unit vector?
The explanation I'm given:
"Remember that two vectors $\vec a$ and $\vec b$ are parallel if
$$\vec a = \lambda \vec b$$
for some scalar $\lambda$.
Also remember that
$|\lambda \vec a| = |\lambda||\vec a| $.
So given a vector $\vec a$, what value of $\lambda$ will give a vector $\vec b = \lambda \vec a$ which has magnitude $1$?
The correct answer is 'True'."
Best Answer
Let $\mathbf{u}$ be a non-unit vector. Set $\mathbf{n} = \mathbf{u}/|\mathbf{u}|$. Then $\mathbf{n}$ is a unit vector and $\mathbf{u}$ is parallel to $\mathbf{n}$ since $\mathbf{u} = |\mathbf{u}| \, \mathbf{n}.$