3D

This week we did a lot of different things with vectors and matrices. They all seemed pretty hard when they were taught but they are actually not that bad and for the first time I was able to fly through one of the homeworks. Here are the 3D notes, which was probably the hardest section for me:

For magnitude: |AB| = squareroot (x2 – x1)^2 + (y2 – y1)^2 + (z2 + z1)^2

Ex: Find |AB| for the points ( 2, 3), (3, 7), (1, 0)
Square root (3-2) ^2 + (7 – 3) ^2 + (0 – 1)^2
1 + 16 -1 = 16
Square root 16 = 4; |AB| = 4

Ex2: Find |AB| for the points (3, 6) , (3, 0 ) , ( 4, 7)
Square root ( 6 – 3 ) ^2 + ( 0 - 3 ) ^2 + ( 7 – 4 ) ^2
9 -9 + 9 = 9
Square root 9 = 3; |AB| = 3