How do you calculate the unit vector?

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Answer 1 · 2018-07-30T23:53:22

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Please read the explanation.

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

Let us examine a vector given below:

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The represented vector is $- - \to O A = 3 ˆ i + 3 ˆ j$ $color(red)(vec(OA)= 3 hat (i)+3 hat (j)$

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

$| O A | = \sqrt{3^{2} + 3^{2}}$ $color(blue)(|OA| = sqrt(3^2+3^2)$

$\Rightarrow \sqrt{18}$ $rArr sqrt(18)$ units.

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

we have to divide the above vector by $\sqrt{18}$ $color(red)(sqrt(18)$

Hence,

$ˆ O A = (\frac{1}{\sqrt{18}}) (3 ˆ i + 3 ˆ j)$ $color(blue)(hat (OA) = (1/sqrt(18))(3 hat i + 3 hat j ))$

This is the unit vector.

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

Hope this helps.