# Vector & Geometry

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if A= i+j, B= 2i-3j+k and C= 4j-3k

find: Ax(BxC)

pls help with solution.

• Vector & Geometry - ,

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 cross-product 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 cross-product 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 cross-product 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 cross-product 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

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