If A=<−3,3,−1> and B=<8,7,2>, what is A⋅B−||A||||B||?

1 Answer
Faizan B.
Feb 6, 2016

−5−√2223≈−52.15

Explanation:

Since A∙B=x1x2+y1y2+z1z2, the A∙B term equals (−3⋅8)+(3⋅7)+(−1⋅2), which is -5.

Since the magnitude of a vector is given by √x2+y2+z2, the magnitude of A is √(−3)2+(3)2+(−1)2, which equals √19.

Likewise, the magnitude of B is √82+72+22, which equals √117

Therefore, the equation A⋅B−||A||||B|| simplifies to −5−√19⋅√117 which further simplifies to −5−√2223, which is approximately -52.15

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