The vectors are
vecA=<5,6>→A=<5,6>
vecB=<-1,7>→B=<−1,7>
vecA+vecB=<5,6> + <-1,7> =<4,13>→A+→B=<5,6>+<−1,7>=<4,13>
The modulus of vecA→A is
||vecA|| = ||<5,6>||=sqrt(5^2+6^2)=sqrt(25+36)=sqrt61∣∣∣∣∣∣→A∣∣∣∣∣∣=||<5,6>||=√52+62=√25+36=√61
The modulus of vecB→B is
||vecB|| = ||<-1,7>||=sqrt((-1)^2+7^2)=sqrt(1+49)=sqrt50∣∣∣∣∣∣→B∣∣∣∣∣∣=||<−1,7>||=√(−1)2+72=√1+49=√50
The modulus of (vecA+vecB)(→A+→B) is
||vecA+vecB||=||<4,13>||=sqrt(4^2+13^2)=sqrt(16+169)=sqrt185∣∣∣∣∣∣→A+→B∣∣∣∣∣∣=||<4,13>||=√42+132=√16+169=√185
Therefore,
||vecA+vecB||-||vecA||-||vecB||=sqrt185-sqrt61-sqrt50=-1.28∣∣∣∣∣∣→A+→B∣∣∣∣∣∣−∣∣∣∣∣∣→A∣∣∣∣∣∣−∣∣∣∣∣∣→B∣∣∣∣∣∣=√185−√61−√50=−1.28
