If A=<5,6> and B=<−1,4>, what is ||A+B||−||A||−||B||?

1 Answer
Steve M
May 5, 2017

∣∣∣∣∣∣−−−−→A+B∣∣∣∣∣∣−∣∣∣∣∣∣→A∣∣∣∣∣∣−∣∣∣∣∣∣→B∣∣∣∣∣∣=√116−√61−√17
=1.1630(4dp)

Explanation:

We have:

→A=⟨5,6⟩

→B=⟨−1,4⟩

So:

−−−−→A+B=⟨4,10⟩

So the norms are:

∣∣∣∣∣∣→A∣∣∣∣∣∣=√52+62
=√25+36
=√61

∣∣∣∣∣∣→B∣∣∣∣∣∣=√(−1)2+42
=√1+16
=√17

And;

∣∣∣∣∣∣−−−−→A+B∣∣∣∣∣∣=√42+102
=√16+100
=√116

Hence:

∣∣∣∣∣∣−−−−→A+B∣∣∣∣∣∣−∣∣∣∣∣∣→A∣∣∣∣∣∣−∣∣∣∣∣∣→B∣∣∣∣∣∣=√116−√61−√17
=1.1630(4dp)

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