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

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Answer 1 · 2018-03-04T07:09:28

The answer is #=-87.5#

The vectors are

#vecA= <3,1,-4>#

#vecB= <-9,4,3>#

The dot product is

#vecA.vecB= <3,1,-4> . <-9,4,3>#

#= (3)*(-9)+(1)*(4)+(-4)*(3) #

#=-27+4-12#

#=-35#

The magnitude of #vecA# is

#||vecA||=|| <3,1,-4>||#

#=sqrt((3)^2+(1)^2+(-4)^2)#

#=sqrt(9+1+16)#

#=sqrt26#

The magnitude of #vecB# is

#||vecB||=|| <-9,4,3>||#

#=sqrt((9)^2+(4)^2+(3)^2)#

#=sqrt(81+16+9)#

#=sqrt106#

Finally,

#vecA.vecB-||vecA||*||vecB||=-35-sqrt26*sqrt106#

#=-35-52.5#

#=-87.5#