## anonymous one year ago Let u = <-4, -3>. Find the unit vector in the direction of u, and write your answer in component form.

1. Michele_Laino

the length of your vector is: $\Large \left\| u \right\| = \sqrt {{{\left( { - 4} \right)}^2} + {{\left( { - 3} \right)}^2}} = \sqrt {16 + 9} = 5$ now you have to divide your vector by its length

2. Michele_Laino

namely, what is: $\Large \frac{u}{{\left\| u \right\|}}$

3. anonymous

how do i put it in component form?? @Michele_Laino

4. Michele_Laino

it is simple: $\Large \frac{u}{{\left\| u \right\|}} = \frac{{ < - 4, - 3 > }}{5} = < \frac{{ - 4}}{5},\frac{{ - 3}}{5} >$

5. Michele_Laino

that procedure above is the division of a vector by a real number, which is always possible when, as in our case, that real number is different from zero

6. anonymous

ohhh okay thank you @Michele_Laino