# How do you calculate the unit vector?

Jul 30, 2018

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#### Explanation:

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A Unit Vector is a vector with a color(red)("magnitude" = 1

Let us examine a vector given below:

The represented vector is color(red)(vec(OA)= 3 hat (i)+3 hat (j)

To find the magnitude of the vector we can use the Pythagoras Theorem:

color(blue)(|OA| = sqrt(3^2+3^2)

$\Rightarrow \sqrt{18}$ units.

To find a unit vector, in the same direction of the above vector,

we have to divide the above vector by color(red)(sqrt(18)

Hence,

$\textcolor{b l u e}{\hat{O A} = \left(\frac{1}{\sqrt{18}}\right) \left(3 \hat{i} + 3 \hat{j}\right)}$

This is the unit vector.

The magnitude of this vector is color(red)(" 1 unit".

Hope this helps.