Vector & Geometry
posted by Mathwise .
if A= i+j, B= 2i3j+k and C= 4j3k
find: Ax(BxC)
pls help with solution.

A=[1,1,0]
B=[2,3,1]
C=[4,0,3]
Let's do BxC
I use a very simple algorith to form the crossproduct of two vectors.
 write the two vectors above each other
2 3 1
4 0 3
 for the first number, with your pinkie or with a pencil, block off the first column and find the right crossproduct of the remaining square matrix, that is, (3)(3)  (0)(1) = 9
for the second number, with your pinkie or withe a pencil, block off the middle column and find the negative right crossproduct of the remaining matrix, that is
( (2)(3)  (1)(4) ) = 10
 and finally for the third number, block off the third column and find the right crossproduct of the remaining square matrix, that is, (2)(0)  (3)(4) = 12
So BxC = [9,10,12]
( I always check by taking the dot product of this with the two original vectors, you should get zero)
Now repeat by taking [1,1,0]x[9,10,12]
I got [12, 12, 1} or 12i  12j + k