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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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