# Let \vec a = \langle 3,5-5 \rangle. Find a unit vector in the same direction as \vec a

## Question:

Let {eq}\vec a = \langle 3,5-5 \rangle {/eq}. Find a unit vector in the same direction as {eq}\vec a {/eq}

## Vector

A quantity that has magnitude as well as direction is known as the vector quantity. The unit vector of any vector is given by the formula {eq}\hat a = \frac{ \vec a}{|\vec a|} {/eq} and the direction of this unit vector is the same as the direction of the vector a.

We have {eq}\vec a=(3,5,-5) {/eq}

The magnitude of this vector is equal to

{eq}= \sqrt((3)^{2}+(5)^{2}+(-5)^{2}) \\ = \sqrt (9+25+25) \\ = \sqrt59 {/eq}

And the unit vector of any vector is given by the formula {eq}\hat a = \frac{ \vec a}{|\vec a|} {/eq}

Thus, unit vector is equal to {eq}(\frac{3}{\sqrt59} , \ \frac{5}{\sqrt59}, \ \frac{-5}{\sqrt59}) {/eq}

Therefore, the unit vector that has the same direction with the given vector is equal to {eq}(\frac{3}{\sqrt59} , \ \frac{5}{\sqrt59}, \ \frac{-5}{\sqrt59}) {/eq}