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Find a unit vector in the direction of the given vector.
v = 9i − 6j

1 Answer

4 votes

Given:

The given vector is:


v=9i-6j

To find:

The unit vector in the direction of the given vector.

Solution:

If a vector is
v=ai+bj, then the unit vector in the direction of the this vector is


\hat v=(v)/(|v|)

Where,
|v|=\sqrt{a^2+b^2

We have,


v=9i-6j

Here,
a=9 and
b=-6. So,


|v|=√(9^2+(-6)^2)


|v|=√(81+36)


|v|=√(117)


|v|=3√(13)

Now, the unit vector in the direction of the given vector is:


\hat v=(9i-6j)/(3√(13))


\hat v=(9i)/(3√(13))-(6j)/(3√(13))


\hat v=(3)/(√(13))i-(2)/(√(13))j

Therefore, the required unit vector is
\hat v=(3)/(√(13))i-(2)/(√(13))j.

User Joe Clay
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