Unformatted text preview: ~ A and its projection on the xyplane, then derived ~ A from the length of the projection and the Pythagorean theorem (applied twice). Vector addition Drew a picture of the parallelogram with sides ~ A and ~ B and showed how the diagonals are ~ A + ~ B and ~ A~ B. Addition works componentwise and indeed ~ A = h a 1 ,a 2 ,a 3 i = a 1 ˆ ı + a 2 ˆ + a 3 ˆ k in our earlier example. Application: Used vector additon to ﬁnd the components of the vector from point P to point Q. Showed that→ PQ =→ OQ→ OP = h q 1p 1 ,q 2p 2 ,q 3p 3 i (where O denotes the origin of the coordinate system). 1...
View
Full Document
 Spring '08
 Helton
 Geometry, Pythagorean Theorem, Vectors, Vector Space, Euclidean geometry

Click to edit the document details