problem01_49 - ^ ^ j B = Bx i + By ^. j 1.49: a) Let A = Ax...

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Unformatted text preview: ^ ^ j B = Bx i + By ^. j 1.49: a) Let A = Ax i + Ay ^, ^ A + B = ( Ax + Bx ) i + ( Ay + By ) ^ j ^ B + A = ( Bx + Ax ) i + ( B y + Ay ) ^ j Scalar addition is commutative, so A + B = B + A A B = Ax Bx + Ay By B A = Bx Ax + By Ay Scalar multiplication is commutative, so A B = B A b) ^ ^ A B = ( Ay Bz - Az B y ) i + ( Az Bx - Ax Bz ) ^ + ( Ax B y - Ay Bx ) k j ^ ^ B A = ( B y Az - Bz Ay ) i + ( Bz Ax - Bx Az ) ^ + ( Bx Ay - B y Ax ) k j Comparison of each component in each vector product shows that one is the negative of the other. ...
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