If A= <2 , 6 >A=<2,6> and B= <-1,6 >B=<−1,6>, what is ||A+B|| -||A|| -||B||||A+B||−||A||−||B||?
1 Answer
Jan 16, 2016
Explanation:
- To find the magnitude of any vector
vecV=< x,y >"→V=<x,y> in the standard form (its tail is at the origin), just apply the formula:
|V|=sqrt(x^2+y^2)|V|=√x2+y2 - To find the sum of two vectors
AA andBB , add the x-coordinates and the y-coordinates separately. vec(A+B)=< 1,12>−−−−→A+B=<1,12> ||A||=sqrt(2^2+6^2)=sqrt(40)||A||=√22+62=√40
||B||=sqrt((-1)^2+6^2)=sqrt(37)||B||=√(−1)2+62=√37
||A+B||=sqrt(1^2+12^2)=sqrt(145)||A+B||=√12+122=√145 ||A+B||−||A||−||B||=" "sqrt(145)-sqrt(40)-sqrt(37)||A+B||−||A||−||B||= √145−√40−√37
=24.45=24.45