Chapter 9.7, Problem 1AYU

To determine

If $\text{u}$ and $\text{v}$ are parallel vectors, then $\text{u} \times \text{v} = 0$.

Answer to Problem 1AYU

Solution:

True.

Explanation of Solution

Given:

If $\text{u}$ and $\text{v}$ are parallel vectors,

Then there is a scalar $\alpha$ such that $\text{u} = \alpha \text{v}$, then

$\text{u} \times \text{v}\left(\alpha \text{v}\right) \times \text{v}$ [since By property: $\alpha \left(\text{u} \times \text{v}\right) = \left(\alpha \text{u}\right) \times \text{v} = \text{v} \times \left(\alpha \text{u}\right)$]

$= \alpha \left(\text{v} \times \text{v}\right) = 0$ [since By property: $\text{v} \times \text{v} = 0$]

Therefore $\text{u} \times \text{v} = 0$

Hence the answer is True.