pmccoy
Answered

Let u= <4,3>. Find the unit vector in the direction of u, and write your answer in component form.

Verified Answer :

lukyo

Take the vector u = <ux, uy> = <4, 3>.

Find the magnitude of u:

||u|| = sqrt[ (ux)^2 + (uy)^2]

||u|| = sqrt[ 4^2 + 3^2 ]

||u|| = sqrt[ 16 + 9 ]

||u|| = sqrt[ 25 ]

||u|| = 5

To find the unit vector in the direction of u, and also with the same sign, just divide each coordinate of u by ||u||. So the vector you are looking for is

u/||u||

u (1/||u||)

= <4, 3> (1/5)

= <4/5, 3/5>

and there it is.

Writing it in component form:

= (4/5) i + (3/5) j

I hope this helps. =)

The component form of the unit vector in the direction of u will be:

\(\rm Unit\; vector\; u = \dfrac{4}{5}\hat{i}+\dfrac{3}{5}\hat{j}\)  and this can be determine by using the unit vector formula.

Given :

u = <4,3>

Unit vector formula will be use to determine the unit vector in the direction of u, that is:

\(\rm Unit\; vector\; u = \dfrac{\overrightarrow {u}}{|\overrightarrow{u}|}\)     ----- (1)

So, the magnitude of u will be:

\(|\overrightarrow{u}| = \sqrt{4^2+3^2}\)

\(|\overrightarrow{u}| = \sqrt{16+9}\)

\(|\overrightarrow{u}| = \sqrt{25}\)

\(|\overrightarrow{u}| = 5\)

Now, put the value of \(\overrightarrow{u}\) and \(|\overrightarrow{u}|\)  in equation (1).

\(\rm Unit\; vector\; u = \dfrac{4\hat{i}+3\hat{j}}{5}\)

\(\rm Unit\; vector\; u = \dfrac{4}{5}\hat{i}+\dfrac{3}{5}\hat{j}\)

So, the component form of the unit vector in the direction of u will be:

\(\rm Unit\; vector\; u = \dfrac{4}{5}\hat{i}+\dfrac{3}{5}\hat{j}\)

For more information, refer the link given below:

https://brainly.com/question/2996997

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