If #A= <2 ,6 ,-3 ># and #B= <-6 ,4 ,7 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2016-05-06T10:53:02

#-9-7sqrt(101)#

This question is vector types.
First, using dot-product since #A.B#

Given #A=<2,6,-3># and #B=<-6,4,7>#

then,

#A.B#=#<2,6,-3>#.#<-6,4,7>#
#A.B#=#(2)(-6)+(6)(4)+(-3)(7)#
#A.B#=#-9#

For #||A|| &||B||# use, #sqrt(a^2+b^2+c^2)# where #a,b,c# are coefficient of vector.

#||A||#=#sqrt(2^2+6^2+(-3)^2)#=#7#
and
#||B||#=#sqrt((-6)^2+4^2+7^2)#=#sqrt(101)#
Since #||A|| . ||B||#=#7sqrt(101)#

#A.B- ||A|| . ||B||#=#-9-7sqrt(101)#