Question

Help with projecting vectors

Answer 1

Find the vector that is orthogonal to the projection vector that comprises the sum of two vector components, if v =-i + 2j and w = 3i − j.

Answer 2

(-1*3)+(2*-1)
-3+-2
-5

Answer 3

\[\frac{ -5 }{ ||3,-1||^2 }(3,-1)\]

Answer 4

\[\frac{ -5 }{ \sqrt10^2 }=\frac{ -5 }{ 10 }(3,-1)\]

Answer 5

(-3/2, 1/2)

Answer 6

shouldnt you sum the two vectors , v + w , first

Answer 7

I am confused

Answer 8

the wording of the question is a bit confusing

Answer 9

the way i read it, the projection vector is the sum of the components of the two vectors, therefore it is the vector sum of the two given vectors

Answer 10

Yes as was the last time i did one like this with this wording.

Find the vector that is orthogonal to the projection vector that comprises the sum of two vector components, if v =-2i + 5j and w = 5i + 4j.

The answer was when we found v2

Answer 11

this particular projection vector happens to be the vector sum of v and w

Answer 12

v2?

Answer 13

so we have to v2=v-v1=

Answer 14

can you take a screen shot of a similar problem

Answer 15

v1= (-3/2, 1/2)

Answer 16

http://openstudy.com/users/darkbluechocobo#/updates/554d0976e4b0a15b79cf38e7

Answer 17

very poorly phrased, whoever wrote this question.

Answer 18

badly phrased

Answer 19

I agree

Answer 20

ok so lets assume they mean the projection of v on w

Answer 21

So to find v2

-i + 2j - (-3/2, 1/2)
-1-(-3/2)
2-1/2

Answer 22

(1/2 ,3/2)

Answer 23

v2=(1/2 ,3/2) and due to the last question that was like this, this should be the answer

Answer 24

I agree the projection of v on w is
-5/sqrt(10) * (3,-1)

Answer 25

what are the multiple choices given

Answer 26

(-3/2, 1/2)

or

(1/2 ,3/2

Answer 27

ok one moment,

Answer 28

projection (v on w) =v.w / |w|^2 * w
v=(-1,2)
w = (3,-1)

therefore
proj (v on w) = -5/10 * ( 3,-1) = ( -3/2, 1/2)

now we have a triangle :
proj (v on w) + n = v
n = proj(v on w) - v

n = v - proj (v on w)
= (-1,2) - ( -3/2, 1/2)
= ( -1 + 3/2, 2 - 1/2)
= ( 1/2, 3/2)

Answer 29

I don't understand why they couldn't have just called it v2 like they did in our lesson. S:

Answer 30

ok so you agree that n = (1/2, 3/2)
different books have different notation, the important thing is to understand the idea, then the notation doesn't really matter.
(of course there is bad notation and poorly phrased statements).