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

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Answer 1 · 2017-11-08T21:43:16

#~~--76.066# ( 3 .d.p.)

#A = ((2),(7),(-4))#

#B= ((-1),(-4),(2))#

#A*B= ((-2),(-28),(-8))=(-2)+(-28)+(-8)=-38#

#||A||= sqrt((2)^2+(7)^2+(-4)^2)=sqrt(69)#

#||B||= sqrt((-1)^2+(-4)^2+(2)^2)=sqrt21#

( we do not need to be concerned with negative roots, since the magnitude is an absolute value )

So we have:

#-38-sqrt69xxsqrt21#

= #-38-3sqrt(23xx7)#

= #-38-3sqrt161#

= #-38-38.06573#

= #-76.066# ( 3 .d.p.)