If A= <-2 ,-7 ,-1 > and B= <3 ,4 ,-8 >, what is A*B -||A|| ||B||?

1 Answer
Dec 14, 2017

The answer is =-95.3

Explanation:

The vectors are

vecA= <-2,-7,-1>

vecB = <3,4,-8>

The modulus of vecA is =||vecA||=||<-2,-7,-1>||=sqrt((-2)^2+(-7)^2+(-1)^2)=sqrt(4+49+1)=sqrt54

The modulus of vecB is =||vecB||=||<3,4,-8>||=sqrt((3)^2+(4)^2+(-8)^2)=sqrt(9+16+64)=sqrt89

Therefore,

||vecA|| xx||vecB||=sqrt(54)*sqrt89=sqrt4806

The dot product is

vecA.vecB= <-2,-7,-1> .<3,4,-8> =(-2xx3)+(-7xx4)+(-1xx-8)=-6-28+8=-26

Therefore,

vecA.vecB-||vecA|| xx||vecB||=-26-sqrt4806= -95.3