Question

Find the unit vector that has the same direction as the vector v.v=

Answer 1

Given a vector:

`v=-6i-8j`

The unit vector is expressed as

`\begin{gathered} \frac{\vec{v}}{\lvert v\rvert} \\ \text{where} \\ \lvert v\rvert\text{ is the magnitude }of\text{ the vector} \end{gathered}`

step 1: Evaluate the magnitude of the vector.

The magnitude of vector v is evaluated as

`\begin{gathered} |v|=\sqrt[]{(-6)^2+(-8)^2} \\ =\sqrt[]{36+64} \\ =\sqrt[]{100} \\ \Rightarrow|v|=10 \end{gathered}`

step 2: Evaluate the unit vector.

`\begin{gathered} \frac{\vec{v}}{\lvert v\rvert}=(1)/(|v|)*\vec{v} \\ =(1)/(10)(-6i-8j) \\ =-(6)/(10)i-(8)/(10)j \\ \Rightarrow-(3)/(5)i-(4)/(5)j \end{gathered}`

Hence, the unit vector that has the same direction as the vector v

is

`-(3)/(5)i-(4)/(5)j`