Question

5.

Let u = <-4, -3>. Find the unit vector in the direction of u, and write your answer in component form. (2 points)

Vector with two components. First component, negative four divided by five. Second component, negative three divided by five.

<1, 1>

Vector with two components. First component, negative four divided by seven. Second component, negative three divided by seven.

Vector with two components. First component, negative four divided by twenty five. Second component, negative three divided by twenty five.

Answer 1

The length of the vector <-4,-3> is

`√((-4)^2+(-3)^2)=√(16+9)=√(25)=5`

So, if we divide the components by 5, we'll get a vector with unitary length:

`v=\left(-(4)/(5), -(3)/(5)\right) \implies |v| = \sqrt{\left(-(4)/(5)\right)^2+\left(-(3)/(5)\right)^2}=\sqrt{(16)/(25)+(9)/(25)}=\sqrt{(25)/(25)}=1`