Projection & vector component

[umbral dew]

Can someone please help me out with this?

[sage stone]

1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
2. Wait patiently for a helper to come along.
3. Once someone helps you, say thank you and close the thread with:

   +close
   

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[sly spoke]

just use the formula

[umbral dew]

Is the answer for a) <7,9> ?

[sly spoke]

no

[umbral dew]

What is it then?

[sly spoke]

compute it and find out

post your work if you want me to check your work...

[umbral dew]

Alright hold on

[sly spoke]

as common sense would dictate

[sly spoke]

yeah that's nonsense

just compute the scalar in front of v, then scale v

It's clear from computation $\frac{u\cdot v}{v\cdot v}=\frac{9\times 1+7\times 3}{1^2+3^2}=\frac{30}{10}=3$

[fluid bronze]

Omegabet_

[umbral dew]

Can you answer in a more respectful way and a bit clearer

[sly spoke]

Explain what isnt clear

I assume you know how to compute dot products

[umbral dew]

I don’t know what you just did

[sly spoke]

I computed the scalar

in the formula

recall the formula

$P_v(u):=\frac{u\cdot v}{v\cdot v}v$

[fluid bronze]

Omegabet_

[sly spoke]

from computation, it's evident (u.v)/(v.v) = 3

so $P_v(u)=3v=(3,9)$

[fluid bronze]

Omegabet_

[umbral dew]

Ohhh ok

I got it

Thank youu

What about b

[sly spoke]

what about it?

[umbral dew]

Is it correct?

[sly spoke]

no

From drawing it, it's clear $u=P_v(u)+z$ where $z\perp v$

[fluid bronze]

Omegabet_

[umbral dew]

Is it (6,-2)?

[sly spoke]

yes.

[umbral dew]

Okk thank youu

[sly spoke]

$z:=u-P_v(u)$

[fluid bronze]

Omegabet_

[umbral dew]

+close