Vector question (the a and b have an arrow on top to represent vector notation) PQRS is a quadrilateral with PQ=2a, QR=3b, and QS=3b-3a. Express PS and RS in terms of a and b

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ishpiro eNotes educator| Certified Educator

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`

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