If #A= <-2 ,-5 ,4 ># and #B= <-7 ,4 ,-9 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2016-10-23T15:10:24

The answer is #vecA.vecB-∥vecA∥∥vecB=-123.1#

First we calculate the dot product
#vecA.vecB=〈-2,-5,4〉.〈-7,4,-9〉=14-20-36=-42#

Then we calculate the modulus of the vectors

#∥vecA∥=sqrt (4+25+16)=sqrt45#

#∥vecB∥=sqrt(49+16+81)=sqrt146#

So the result is #vecA.vecB-∥vecA∥∥vecB∥=-42-sqrt(45*146)=-42-81.1=-123.1#