Question

Vector u has a magnitude of 5 units, and vector v has a magnitude of 4 units. Which of these values are possible for the magnitude of u + v?

Answer 1

Answer:

Remember the triangular inequality says that if u and v are vectors then

$\lvert\lvert u + v \lvert\lvert \leq \lvert\lvert u \lvert\lvert +\lvert\lvert v\lvert\lvert$

Since the magnitude always is a nonnegative number and the magnitude of u is 5 units and the magnitude of v is 4 units ,

$0\leq \lvert\lvert u + v\lvert\lvert \leq \lvert\lvert u \lvert\lvert + \lvert\lvert v\lvert\lvert = 5+ 4 =9$

Then possibles values for the magnitude of u +v  are in the interval $[0,9]$