The maximum and minimum magnitudes of the resultant of two given vectors are 17N and 7N respectively. If two vectors are at right angles to each other, then find the magnitude of their resultant?
A + B = 17
A - B = 7
2A=24
A = 12
B = 5
so
sqrt(25+144)
To find the magnitude of the resultant of two vectors at right angles to each other, we can use the Pythagorean theorem. According to the theorem, the square of the magnitude of the resultant vector (R) is equal to the sum of the squares of the magnitudes of the two individual vectors (A and B), assuming they are at right angles to each other.
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.