If A=<−5,3,−3> and B=<2,2,8>, what is A⋅B−||A||||B||?

1 Answer
sente
Dec 28, 2016

A⋅B−||A||||B||=−28−6√86≈−83.64

Explanation:

Given vectors →x=<x1,x2,x3> and →y=<y1,y2,y3>, we have

→x⋅→y=x1y1+x2y2+x3y3

and

∣∣∣∣→x∣∣∣∣=√x21+x22+x23

Using these on the given vectors, we have

A⋅B=−5(2)+3(2)+(−3)(8)=−10+6−24=−28

and

||A||||B||=√(−5)2+32+(−3)2⋅√22+22+82

=√43⋅√72

=6√86

so, taken together

A⋅B−||A||||B||=−28−6√86≈−83.64

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