Question

find the vector v sith the given magnitude and the samd direction as u. magnitude= 5 direction=<3,3>

Answer 1

well, the given vector direction needs to be a unit vector (length 1) so that we can multiply it by 5 to get it to a length of 5

Answer 2

other than that, we can determine this is a 45 degree vector that has 1-1-sqrt(2) ratio to begin with

when sqrt(2) = 5 that means we multiply the sides by 5/sqrt(5)

Answer 3

err... 5/sqrt(2) that is

Answer 4

It says the answer is <5sqrt2/2, 5sqrt2/2> I just do not know how to get to the answer exactly

Answer 5

the key is knowing how to unit a vector ...

if we have a vector of a given length; say its 9 inches long. How would you divide this up into pieces that are 1 inch long?

Answer 6

9/9 = 1 right? so we would divide it by its own length. this works for any length to get it to a unit value.

Answer 7

how do we determine the length of a given vector?

Answer 8

with the distance formula? but i dont even know if that is right

Answer 9

would i steer you wrong?

Answer 10

haha im sorry my teacher is terrible!

Answer 11

use the distance formula on your <3,3> and lets see what we get :)

Answer 12

sqrt 18

Answer 13

good, or simplified as 3 sqrt(2)

when we want to unit a vector, divide itself by its own length

\[\frac{1}{3\sqrt{2}}<3,3>=<\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}>\]

right?

Answer 14

im sorry but where did the 1/sqrt2 come in?

Answer 15

some books hate it when we have sqrts on the bottom, so they like to rewrite them:\[\frac{1}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}\]

Answer 16

\[\sqrt{18}=\sqrt{9*2}=3\sqrt{2}\]
use this to divide off the vector; scale i ...

\[\frac{1}{3\sqrt{2}}<3,3>=<\frac{\cancel{3}}{\cancel{3}\sqrt{2}},\frac{\cancel{3}}{\cancel{3}\sqrt{2}}>\]

Answer 17

oh i get it now! thank you so much!!

Answer 18

youre welcome :)