If A= <8 ,1 ,-4 >A=<8,1,−4> and B= <-2 ,4 ,3 >B=<−2,4,3>, what is A*B -||A|| ||B||A⋅B−||A||||B||?

1 Answer
Narad T.
Nov 1, 2016

The answer is =-24-9sqrt29=−24−9√29

Explanation:

The dot product vecA.vecB=〈8,1,-4〉.〈-2,4,3〉=-16+4-12=-24→A.→B=⟨8,1,−4⟩.⟨−2,4,3⟩=−16+4−12=−24
Modulus of vecA→A =∥〈8,1,-4〉∥=sqrt(64+1+16)=sqrt81=9=∥⟨8,1,−4⟩∥=√64+1+16=√81=9
Modulus of vecB→B =∥〈-2,4,3〉∥=sqrt(4+16+9)=sqrt29=∥⟨−2,4,3⟩∥=√4+16+9=√29

And finally vecA.vecB-∥vecA∥∥vecB∥=-24-9sqrt29→A.→B−∥→A∥∥→B∥=−24−9√29

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