If A= <-2, 2 >A=<−2,2> and B= <9, 4>B=<9,4>, what is ||A+B|| -||A|| -||B||||A+B||−||A||−||B||?

1 Answer
ali ergin
Mar 19, 2016

||A+B|| - ||A-B||=sqrt85-sqrt125||A+B||−||A−B||=√85−√125

Explanation:

A+B=CA+B=C
C_x=A_x+B_x=-2+9=7Cx=Ax+Bx=−2+9=7
C_y=A_y+B_y=2+4=6Cy=Ay+By=2+4=6
||C||=sqrt(C_x^2+C_y^2)" "||C||=sqrt(7^2+6^2)=sqrt(49+36)||C||=√C2x+C2y ||C||=√72+62=√49+36
||C||=sqrt85||C||=√85

A-B=DA−B=D
D_x=A-x-B_x=-2-9=-11Dx=A−x−Bx=−2−9=−11
D_y=A_y-B_y=2-4=-2Dy=Ay−By=2−4=−2
||D||=sqrt( D x^2+ D y^2)" "||D||=sqrt((-11)^2+(-2)^2)||D||=√Dx2+Dy2 ||D||=√(−11)2+(−2)2
||D||=sqrt(121+4)" "||D||=sqrt125||D||=√121+4 ||D||=√125
||A+B|| - ||A-B||=||C||-||D||||A+B||−||A−B||=||C||−||D||
||A+B|| - ||A-B||=sqrt85-sqrt125||A+B||−||A−B||=√85−√125

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