If #A= <-1 ,6 ,-4 ># and #B= <7 ,2 ,4 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2016-12-15T07:10:49

The answer is #=-71.5#

#vecA=〈-1,6,-4〉#

#vecB=〈7,2,4〉#

The dot product is #vecA.vecB=〈-1,6,-4〉.〈7,2,4〉#

#=-7+12-16=-11#

The modulus of #vecA# is #=∥vecA∥=∥〈-1,6,-4〉∥#

#=sqrt(1+36+16)=sqrt53#

The modulus of #vecB# is #=∥vecB∥=∥〈7,2,4〉∥#

#=sqrt(49+4+16)=sqrt69#

Therefore,

#vecA.vecB-∥vecA∥*∥vecB∥=-11-sqrt53*sqrt69#

#=-11-60.5=-71.5#