A + B = 17
A - B = 7
2A=24
A = 12
B = 5
so
sqrt(25+144)
A - B = 7
2A=24
A = 12
B = 5
so
sqrt(25+144)
In this case, let's assume that the magnitudes of the given vectors are A and B. We are given that the maximum magnitude of the resultant is 17N and the minimum magnitude of the resultant is 7N. Therefore, we have the following equation:
R^2 = A^2 + B^2
Given that A and B are at right angles to each other, we know that the resultant magnitude can vary between the maximum and minimum values. Hence, we can write two equations to solve for A and B:
1. For the maximum magnitude:
17^2 = A^2 + B^2 (equation 1)
2. For the minimum magnitude:
7^2 = A^2 + B^2 (equation 2)
Now we have a system of equations with two unknowns (A and B). We can solve these equations to find the values of A and B.
Subtracting equation 2 from equation 1, we get:
17^2 - 7^2 = A^2 + B^2 - (A^2 + B^2)
289 - 49 = A^2 + B^2 - A^2 - B^2
240 = 0
This is an invalid equation, which means there is no solution.
Therefore, there is no combination of vectors A and B that would result in a maximum magnitude of 17N and a minimum magnitude of 7N when they are at right angles to each other.