If #A= <-2 ,3 ,-4 ># and #B= <-9 ,4 ,8 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2018-01-04T15:28:45

The answer is #=-70.3#

The dot product is

#A.B= <-2,3,-4> . <-9,4,8> = (-2*-9)+(3*4)+(-4*8) =18+12-32= -2#

The modulus of #vecA# is

#=||vecA|| =|| <-2,3,-4> || =sqrt((-2)^2+(3)^3+(-4)^2)=sqrt(4+9+16)=sqrt(29)#

The modulus of #vecB# is

#=||vecB|| =|| <-9,4,8> || =sqrt((-9)^2+(4)^3+(8)^2)=sqrt(81+16+64)=sqrt(161)#

Therefore,

#A.B-||vecA||*||vecB||=-2-sqrt29*sqrt161=-70.3#