How do you calculate the unit vector?

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Answer 1 · 2018-07-30T23:53:22

#" "#
Please read the explanation.

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

Let us examine a vector given below:

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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)#

#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 #color(red)(sqrt(18)#

Hence,

#color(blue)(hat (OA) = (1/sqrt(18))(3 hat i + 3 hat j ))#

This is the unit vector.

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

Hope this helps.