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

The possible value of the magnitude of u + v is 9 units

How to determine the magnitude of u + v?

From the question, we have the following parameters that can be used in our computation:

Vector u has a magnitude of 5 units, and vector v has a magnitude of 4 units

This means that

|u| = 5

|v| = 4

The magnitude of u + v is

|u + v| = 5 + 4

Evaluate

|u + v| = 9

Hence, the magnitude of u + v is 9

Answer 2

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]`