Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

ohhh okay thank you @Michele_Laino