Question

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

Answer 1

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. =)

Answer 2

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