As you can see from the attached image, the vector `vec(PS)` can be expressed as the sum of two given vectors: `vec(PS) = vec(PQ)+vec(QS)` .
Then we can plug in the expressions for `vec(PQ)` and `vec(QS)` in terms of `veca` and `vec b` , which will give us
`vec(PS) = 2veca + 3vecb - 3veca = -veca+3vecb` .
The vector `vec(RS)` is a little trickier, because it has to be expressed as a difference of two vectors:
`vec(RS) = vec(QS)-vec(QR)` (This can be checked by addition: if you consider `vec(QS)` , you can see from the image that `vec(QS) = vec(QR) + vec(RS)` .
Again, plug in the appropriate expressions for the two given vectors in terms of `veca ` and `vecb` and simplify:
`vec(RS) = (3vecb - 3veca) - 3vecb = -3veca`