anonymous
  • anonymous
Let u = <-4, -3>. Find the unit vector in the direction of u, and write your answer in component form.
Mathematics
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SOLVED
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chestercat
  • chestercat
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Michele_Laino
  • 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
Michele_Laino
  • Michele_Laino
namely, what is: \[\Large \frac{u}{{\left\| u \right\|}}\]
anonymous
  • anonymous
how do i put it in component form?? @Michele_Laino

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Michele_Laino
  • Michele_Laino
it is simple: \[\Large \frac{u}{{\left\| u \right\|}} = \frac{{ < - 4, - 3 > }}{5} = < \frac{{ - 4}}{5},\frac{{ - 3}}{5} > \]
Michele_Laino
  • 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
anonymous
  • anonymous
ohhh okay thank you @Michele_Laino

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