Vectors question

1. Nov 16, 2015

Eysz

NOTE: Thread was moved to Homework forums and thus has no homework template...

I managed to find (a) but i couldn't figure out (b).

I think OR = OP + PR = (2/3)a + t( (-1/15)a + (2/5)b) but i don't know how to go further please guide or help me with this please. Thanks

2. Nov 16, 2015

haruspex

There's a useful, directly observable, relationship between $\vec{OR}$ and b.

3. Nov 16, 2015

Eysz

Then i should just substitute t=10 into the OR= (2/3)a + t( (-1/15)a + (2/5)b) since the answer must be in terms of b. That would make it 4b.

Is it correct?

4. Nov 16, 2015

haruspex

Yes, but not because you are told the answer must be in terms of b. You know from the diagram that it must be in the direction of b. Unless a and b are in the same direction, how else will you get (2/3)a + t( (-1/15)a + (2/5)b) to be a scalar multiple of b?

5. Nov 17, 2015

Eysz

I completely understand now! Thanks!