The vectors are
vecA= <2,7,-4>→A=<2,7,−4>
vecB = <-1,-9,2>→B=<−1,−9,2>
The modulus of vecA→A is =||vecA||=||<2,7,-4>||=sqrt((2)^2+(7)^2+(-4)^2)=sqrt(4+49+16)=sqrt69=∣∣∣∣∣∣→A∣∣∣∣∣∣=||<2,7,−4>||=√(2)2+(7)2+(−4)2=√4+49+16=√69
The modulus of vecB→B is =||vecB||=||<-1,-9,2>||=sqrt((-1)^2+(-9)^2+(2)^2)=sqrt(1+81+4)=sqrt86=∣∣∣∣∣∣→B∣∣∣∣∣∣=||<−1,−9,2>||=√(−1)2+(−9)2+(2)2=√1+81+4=√86
Therefore,
||vecA|| *||vecB||=sqrt69*sqrt86=sqrt5934∣∣∣∣∣∣→A∣∣∣∣∣∣⋅∣∣∣∣∣∣→B∣∣∣∣∣∣=√69⋅√86=√5934
The dot product is
vecA.vecB= <2,7,-4> .<-1,-9,2>→A.→B=<2,7,−4>.<−1,−9,2>
=(2xx-1)+(7xx-9)+(-4xx2)=(2×−1)+(7×−9)+(−4×2)
=-2-63-8=-73 =−2−63−8=−73
Therefore,
vecA.vecB-||vecA|| xx||vecB||=-73-sqrt5934= -150.03→A.→B−∣∣∣∣∣∣→A∣∣∣∣∣∣×∣∣∣∣∣∣→B∣∣∣∣∣∣=−73−√5934=−150.03
