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?

There is more than one answer...

1
9
11
13

hey are just sides of a (possible degenerate) triangle, so

5-4 <= |u+v| <= 5+4

To find the possible values for the magnitude of u + v, we need to look at the properties of vector addition.

The magnitude of the sum of two vectors can be determined using the Triangle Inequality. According to this inequality, for any two vectors u and v, the magnitude of their sum will always be less than or equal to the sum of their individual magnitudes. Mathematically, this can be expressed as:

|u + v| ≤ |u| + |v|

In this case, we know that the magnitude of vector u is 5 units and the magnitude of vector v is 4 units. So, we can rewrite the inequality as:

|u + v| ≤ 5 + 4

Simplifying further, we have:

|u + v| ≤ 9

Therefore, any value less than or equal to 9 can be the magnitude of u + v. From the given answer choices, 1, 9, and 13 are possible values.

So, the possible values for the magnitude of u + v are:
1
9
13