Question

What is the best approximation of the projection of (5,-1) onto (2,6)?

A. 0.15(2,6)

B. 0.10(2,6)

C. 0.15(5,-1)

D. 0.10(5,-1)

@ash2326 :)

Answer 1

find the cosine of the angle between them, find the length of (5,-1), and unit out the (2,6)

Answer 2

how do i do that?

Answer 3

\[proj_u~v\]
\[cos(a)=\frac{u\cdot v}{|u||v|}\]
\[|u|cos(a)=\frac{u\cdot v}{|v|}\]
this is the length of the projection

the direction is in the same direction as v, but we have to unit v by dividing out its length
\[\frac{|u|cos(a)}{|v|}=\frac{u\cdot v}{|v|^2}\]

Answer 4

okay :)

Answer 5

so we already know it has to go in the direction of 2,6 so that narrows it down

Answer 6

so its between A and B then?

Answer 7

all you really have to determine now is u.v and |v|

Answer 8

yes

Answer 9

how do i determine u x v and IvI ?

and the IvI is definitely positive though right? cuz of the absolute value bars?

Answer 10

|v| = sqrt( vx^2 + vy^2)

|v|^2 = vx^2 + vy^2

Answer 11

square the parts and add em ...

Answer 12

is vx= 5 and vy=-1?

Answer 13

no, thats "u" :)

Answer 14

ah darn :(

okay so vx=2 and vy=6 ?

Answer 15

ye

Answer 16

so 2^2+6^2= 4+36 = 40 ?

Answer 17

thats our denominator so far so good

Answer 18

okay :) yay!

Answer 19

think of |v|^2 as v.v your just multiplying like component parts and adding

u.v is multiplying like component parts and adding

Answer 20

okay :) i'll try to remember that! so are we looking for the numerator now? :O

Answer 21

v: 2,6
dot v: 2,6
-----------
40 = 4+36



u: 5,-1
dot v: 2, 6
-----------
4 = 10-6

Answer 22

okay :) so what do i do from there? :O

Answer 23

|u|cos(a)|v|=u⋅v|v|2 do i apply it to this? the equation u put above^^ ?

Answer 24

sorry, not good at latex :(

Answer 25

we just determined all the parts needed:

u.v = 4
|v|^2 = 40

and we already know the direction of v is required:

what then is 4/40?

Answer 26

okay.. 4/40= .1 ?

Answer 27

then all thats left is to pick the correct option

Answer 28

so the answer is B. 0.10(2,6) ?? :O

Answer 29

thats what i would go with yes

Answer 30

awesome!! :) thank you so much!!! :D

Answer 31

youre welcome, and good luck

Answer 32

thank you!! :)