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?
I believe there are more than one answers:
A: 1 Unit
B: 9 units
C: 11 Units
D: 13 Units
If they have the same direction, then their magnitude is 9
It is also possible to have a triangle with sides 4,5, and 1
clearly not with sides 11 or 13
so A and B
To find the possible values for the magnitude of the sum of vectors u and v, we need to consider the range of possible magnitudes based on the given magnitudes of u and v.
The magnitude of a vector sum is generally determined through vector addition. In this case, since the magnitudes of vectors u and v are given and they are not parallel to each other, we can use the triangle inequality to determine the possible magnitudes of their sum.
According to the triangle inequality, for any two vectors u and v, the magnitude of their sum (u + v) must be less than or equal to the sum of their individual magnitudes.
Therefore, we can determine the possible range of magnitudes for u + v by adding the magnitudes of u and v:
5 + 4 = 9
This means that the magnitude of u + v can be at most 9 units. So, option B: 9 units is a valid answer.
Since we want to find all the possible values, we also need to consider the lower limit. To find the smallest possible magnitude for u + v, we need to subtract the smaller magnitude from the greater magnitude:
5 - 4 = 1
Therefore, the smallest possible magnitude of u + v is 1 unit. So, option A: 1 unit is also valid.
To summarize, the possible values for the magnitude of u + v are:
A: 1 unit
B: 9 units
Therefore, the correct answers are options A and B.
To find the possible values for the magnitude of u + v, we can use the triangle inequality, which states that the magnitude of the addition of two vectors is less than or equal to the sum of their magnitudes.
Given that the magnitude of vector u is 5 units and vector v is 4 units, we can determine the range of possible values for the magnitude of u + v.
The minimum possible magnitude of u + v occurs when the vectors are in opposite directions. In this case, the magnitude of u + v would be |5 - 4| = 1 unit.
The maximum possible magnitude of u + v occurs when the vectors are in the same direction. In this case, the magnitude of u + v would be |5 + 4| = 9 units.
Therefore, the possible values for the magnitude of u + v are 1 unit and 9 units.
So, the correct answer is:
A: 1 unit
B: 9 units