The resultant of two force x and y will be least when the angle between x and y?
The resultant of two forces x and y will be least when the angle between them is 180 degrees or when they are opposite to each other. In this case, the forces will be cancelling each other's effect and the resultant will be the difference between the magnitudes of the two forces.
To find the angle between the two forces (x and y) that will result in the least resultant force, we can use the concept of vector addition.
The resultant force (R) of two forces (x and y) can be calculated using the vector addition formula:
R = sqrt(x^2 + y^2 + 2xy * cosθ)
Here, θ represents the angle between the vectors x and y.
To find the angle that will result in the least resultant force, we need to minimize the value of R. This can be done by finding the minimum value of the expression inside the square root.
Since x, y, and cosθ are all positive quantities, to minimize the value of the expression, we want the term 2xy * cosθ to be as small as possible.
To make 2xy * cosθ as small as possible, we need cosθ to be as close to -1 as possible. The value of cosθ becomes -1 when θ is equal to 180 degrees (π radians).
Therefore, the angle between x and y that will result in the least resultant force is 180 degrees or π radians.