The vectors are
vecA= <-3,6>→A=<−3,6>
vecB = <-2,5>→B=<−2,5>
The modulus of vecA→A is =||vecA||=||<-3,6>||=sqrt((-3)^2+(6)^2)=sqrt(9+36)=sqrt45=∣∣∣∣∣∣→A∣∣∣∣∣∣=||<−3,6>||=√(−3)2+(6)2=√9+36=√45
The modulus of vecB→B is =||vecB||=||<-2,5>||=sqrt((-2)^2+(5)^2)=sqrt(4+25)=sqrt29=∣∣∣∣∣∣→B∣∣∣∣∣∣=||<−2,5>||=√(−2)2+(5)2=√4+25=√29
The modulus of (vecA+vecB)(→A+→B) is
||vecA+vecB||= ||<-3,6,> +<-2,5>|| =||< -5,11>||∣∣∣∣∣∣→A+→B∣∣∣∣∣∣=||<−3,6,>+<−2,5>||=||<−5,11>||
=sqrt((-5)^2+11^2)=√(−5)2+112
=sqrt(25+121)=√25+121
=sqrt146=√146
Therefore,
||vecA+vecB||-||vecA|| -||vecB||=sqrt(146)-sqrt(45)-sqrt(29)= -0.01∣∣∣∣∣∣→A+→B∣∣∣∣∣∣−∣∣∣∣∣∣→A∣∣∣∣∣∣−∣∣∣∣∣∣→B∣∣∣∣∣∣=√146−√45−√29=−0.01
