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

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Answer 1 · 2018-08-07T19:01:32

#A*B-||A||||B|| ~~ -16.15#

Here,

#A=<3,1,-2> and B= <4,-2,3>#

Now , #A*B=<3,1,-2> * <4,-2,3 #

#=>A*B=(3)(4)+(1)(-2)+(-2)(3)=12-2-6=4#

#||A||=sqrt((3)^2+(1)^2+(-2)^2)=sqrt(9+1+4)=sqrt14#

#||B||=sqrt((4)^2+(-2)^2+(3)^2)=sqrt(16+4+9)=sqrt29#

So ,

#A*B-||A||||B||=4-sqrt14sqrt29=4-sqrt406#

#:.A*B-||A||||B|| ~~ -16.15#