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

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Find a unit vector in the direction of the given

Ответ:

fefebat

10.05.2021

Mathematics

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

$\hat v=\dfrac{v}{|v|}$

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

We have,

v=9i-6j

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

$|v|=\sqrt{9^2+(-6)^2}$

$|v|=\sqrt{81+36}$

$|v|=\sqrt{117}$

$|v|=3\sqrt{13}$

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

$\hat v=\dfrac{9i-6j}{3\sqrt{13}}$

$\hat v=\dfrac{9i}{3\sqrt{13}}-\dfrac{6j}{3\sqrt{13}}$

$\hat v=\dfrac{3}{\sqrt{13}}i-\dfrac{2}{\sqrt{13}}j$

Therefore, the required unit vector is $\hat v=\dfrac{3}{\sqrt{13}}i-\dfrac{2}{\sqrt{13}}j$ .

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

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