If A=<−8,3,−1> and B=<−3,4,3>, what is A⋅B−||A||||B||?

1 Answer
Faizan B.
Feb 6, 2016

33−√2516≈−17.16

Explanation:

Since A∙B=x1x2+y1y2+z1z2, the A∙B term equals (−8⋅−3)+(3⋅4)+(−1⋅3), which is 33.

Since the magnitude of a vector is given by √x2+y2+z2, the magnitude of A is √(−8)2+32+(−1)2, which equals √74.

Likewise, the magnitude of B is √(−3)2+42+32, which equals √34

Therefore, the equation A⋅B−||A||||B|| simplifies to 33−√74⋅√34 which further simplifies to 33−√2516, which is approximately -17.16

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