1. ## Scalar Multiplication

Use the diagram to express each of the given vectors in terms of OP and OQ.

a) OR
b) OU
c) OW
d) OS
e) OA
f) OY

Please any help on how to begin this is really appreciated.

Use the diagram to express each of the given vectors in terms of OP and OQ.

a) OR
I get

OR = OP +PR

OR = OP +1/2 PS

As PS = OR then

OR = OP +1/2 OR

Do you follow?

3. Yes I think so!

So then:
OU = OP + PU
OU = OP + 2OQ

But then?

OW = OP + 2OP?

So then:
OU = OP + PU
OU = OP + 2OQ
Yep!

But then?

OW = OP + 2OP?
Nah, I say

OW = OQ + QX +XW

OW = OQ + 2OP + 1/2 OQ

OW = 2OP+3/2 OQ

5. Looking at your picture, I see that OR goes down exactly as much as OP and to the right half as much as OQ. That tells me that OR= OP+ (1/2)OQ.

I see that OS goes down as far as OP and to the right as far as OQ: OS= OP+ OQ.

I see that OA and OW both extend down twice as far as OP so both will require "2OP". OA extends as far to the right as OQ while OW extends to the right 3/2 as far as OQ.

OY extends downward three times as far as OP and to the right exactly as far as OQ. OY= what?