If A=<3,−1> and B=<9,4>, what is ||A+B||−||A||−||B||?

1 Answer
Narad T.
Nov 21, 2017

The answer is =−0.64

Explanation:

The vectors are

→A=<3,−1>

→B=<9,4>

The modulus of →A is =∣∣∣∣∣∣→A∣∣∣∣∣∣=||<3,−1>||=√32+(−1)2=√9+1=√10

The modulus of →B is =∣∣∣∣∣∣→B∣∣∣∣∣∣=||<9,4>||=√92+(4)2=√81+16=√97

→A+→B=<3,−1>+<9,4>=<12,3>

The modulus of →A+→B is =∣∣∣∣∣∣→A+→B∣∣∣∣∣∣=||<12,3>||=√122+(3)2=√144+9=√153

Therefore,

∣∣∣∣∣∣→A+→B∣∣∣∣∣∣−∣∣∣∣∣∣→A∣∣∣∣∣∣−∣∣∣∣∣∣→B∣∣∣∣∣∣=√153−√10−√97=−0.64

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