If #A= <3 ,1 ,-4 ># and #B= <-9 ,1 ,3 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2016-05-02T09:39:48

#A*B-||A||||B||=-86.64#

As #A=<3,1,-4># and #B=<-9,1,3>#

#A*B=(3xx(-9)+1xx1+(-4)xx3)=(-27+1-12)=-38#

#||A||||B||=sqrt(3^2+1^2+(-4)^2)xxsqrt((-9)^2+1^2+3^2)#

= #sqrt(9+1+16)xxsqrt(81+1+9)#

= #sqrt26xxsqrt91#

= #sqrt(2xx13xx13xx7)=13sqrt14=48.64#

Hence #A*B-||A||||B||=-38-48.64=-86.64#