Question

# Use a diagram to prove/explain the following.

1. Prove that for any vectors and , | a+b | less than or equal to |a| + |b|.
2. Is it possible to have |a +b | > |a| + |b|? Explain.
3. Two vectors have the magnitudes 5km and 10km. What are the maximum and minimum magnitudes of their vector sum?

Answer 1

If you prove 1, 2 is not possible

Answer 2

Thoughts on how you might prove 1?

Answer 3

| a+b | is the resultant rite??

Answer 4

of |a| + |b|

Answer 5

help ppls

Answer 6

No, imagine that:

a = <2,3>
b = <-1,3>

\[|a| = \sqrt{2^2 + 3^2} = \sqrt{13}\]
\[|b| = \sqrt{(-1)^2 + 3^2} = \sqrt{10}\]
\[|a| + |b| = \sqrt{13} + \sqrt{10}\]
\[|a+b| = |<1,6>| = \sqrt{1^2 + 6^2} = \sqrt{37}\]
\[\sqrt{37} < \sqrt{13} + \sqrt{10}\]\[\implies |a+b| < |a| + |b|\]

But that just shows for this one case, you need to prove/explain generally.