# Vectors: simplify equation.

• Oct 9th 2010, 10:15 AM
Evaldas
Vectors: simplify equation.
Simplify equation (all are vectors):
(XY - YZ) - (ZT + XT) + (ZY - ZT)
The given answer is 3TY, but I don't know how to get that answer. Please help. For example I'd say that XY - YZ = -YX - YZ = ZX, but that's not TY... Then I'd say ZT - XT = -ZT + XT = ZX(also not TY), then ZY - ZT = TY. So that would be ZX - ZX + TY = TY (not 3TY)
• Oct 9th 2010, 12:41 PM
Opalg
Quote:

Originally Posted by Evaldas
Simplify equation (all are vectors):
(XY - YZ) - (ZT + XT) + (ZY - ZT)
The given answer is 3TY, but I don't know how to get that answer. Please help. For example I'd say that XY - YZ = -YX - YZ = ZX, but that's not TY... Then I'd say ZT - XT = -ZT + XT = ZX(also not TY), then ZY - ZT = TY. So that would be ZX - ZX + TY = TY (not 3TY)

Step 1. Get rid of the parentheses: XY – YZ – ZT – XT + ZY – ZT.

Step 2. Get rid of all the minus signs, using the fact that –AB = BA.

Step 3. Group the six vectors into three pairs and combine each pair into a single vector, using the fact that AB + BC = AC (you'll have to rearrange the order of the six vectors to get them to pair up properly).
• Oct 9th 2010, 12:50 PM
emakarov
One method is to represent every vector in this expression as the difference of two vectors with the beginning at the origin O. E.g., XY = OY - OX, ZT = OT - OZ, etc. Then one has to add like terms to get 3OY - 3OT = 3TY.
• Oct 9th 2010, 12:52 PM
Evaldas
Done! Thank you very much!
XY + ZY + TZ + TX + ZY + TZ = (TZ + ZY) + (TX + XY) + (TZ + ZY) = TY + TY + TY = 3TY.