- #1

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I did:

Let u=[a,b]

Let v=[c,d]

Let |u|=2|v

u.v=ac+bd=0

|u+v|=|u|^2 + |v|^2

But |u|=2|v|

|u+v|=5|v|^2

5|v|^2=100

|v|^2=20

Im stuck after this

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- Thread starter PiRsq
- Start date

- #1

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I did:

Let u=[a,b]

Let v=[c,d]

Let |u|=2|v

u.v=ac+bd=0

|u+v|=|u|^2 + |v|^2

But |u|=2|v|

|u+v|=5|v|^2

5|v|^2=100

|v|^2=20

Im stuck after this

- #2

Hurkyl

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Anyways, can you write |v|^2 in terms of a, b, c, and d? Do you know what |u|^2 is? Have you used the fact that u + v = [6, 8] yet?

- #3

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So

|u|^2+|v|^2=|u+v|^2

But since |u|^2=4|v|^2

5|v|^2=36+64

|v|^2=20

now where can I go?

|u|^2+|v|^2=|u+v|^2

But since |u|^2=4|v|^2

5|v|^2=36+64

|v|^2=20

now where can I go?

- #4

Hurkyl

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- #5

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|v|^2 = c^2+d^2

|v|^2 = 1/2 (a^2 + b^2)

1/2(a^2+ b^2)= c^2 + d^2

Is that what you mean?

|v|^2 = 1/2 (a^2 + b^2)

1/2(a^2+ b^2)= c^2 + d^2

Is that what you mean?

- #6

Hurkyl

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Can you think of anything better you can do with those first two equatinos?

- #7

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|v|^2 = c^2+d^2

|u|^2 = 1/2 (c^2 + d^2)

|u|^2 + |v|^2 = 100

3/2 (c^2 + d^2) = 100

I dont know where Im headed

- #8

Hurkyl

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what formulas do you have involving |v|^2?

- #9

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Projection of u on v

u on v = [u.v/|v|^2] |v|

u on v = [u.v/|v|^2] |v|

- #10

Hurkyl

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You know that your goal is to find 4 equations involving only a, b, c, d which you can solve, right?

- #11

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4 equations?? I didnt know that...I've been focusing on finding a and b

- #12

Hurkyl

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Sometimes you can get lucky and you can find two equations that involve only a and b, but in general that won't happen (and I'm pretty sure it doesn't here)...

You've already found one good equation:

ac + bd = 0

You just need 3 more! You can get 2 more equations out of what you've told me about |v|^2...

Oh, BTW, if |u| = 2|v|, then |u|^2 = 4|v|^2

- #13

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Ill try this and post a little later, thanks man

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