Chapter 6.3, Problem 4E

To determine

To fill: Fill in the blanks to complete the given statements.

Answer to Problem 4E

Two vectors are equivalent when they have the same magnitude and same direction.

Explanation of Solution

Given information: Two equivalent vectors.

Let $\overrightarrow{u}$ be the vector representation by the directed line segment from $P\left(2,4\right)$ to $Q\left(6,5\right)$

And $\overrightarrow{v}$ be the vector representation by the directed line segment from $O\left(0,0\right)$ to $R\left(4,1\right)$

Then the direction of $\overrightarrow{u}$ is $\overrightarrow{PQ}$ and direction of $\overrightarrow{v}$ is $\overrightarrow{OR}$ both in same direction.

Also from distance formula the distance between PQ and OR is $\sqrt{17}$

Therefore, $\overrightarrow{u}$ and $\overrightarrow{v}$ are equivalent vector.