Two vector of 5N and 6N flow they oriented to get the resultant of 7N,9N?( please solve this question)
To solve this question, we need to find the vector components of the given vectors and then add them together to find the resultant vector.
Let's denote the first vector as A and the second vector as B. We are given that A has a magnitude of 5N and B has a magnitude of 6N. We also know the magnitudes of the resultant vector, which are 7N and 9N.
To find the components of A and B, we need to decompose them into their horizontal (x) and vertical (y) components. We can do this by using trigonometry.
Let's assume the angle between vector A and the x-axis is α, while the angle between vector B and the x-axis is β.
For vector A:
Ax = 5N * cos(α)
Ay = 5N * sin(α)
For vector B:
Bx = 6N * cos(β)
By = 6N * sin(β)
Now, since we want to find the resultant vector, which has magnitudes of 7N and 9N, we need to find the sum of the x and y components of A and B.
Rx = Ax + Bx
Ry = Ay + By
To find the magnitude of the resultant vector (R), we can use the Pythagorean theorem:
R^2 = Rx^2 + Ry^2
Now, let's suppose the angle between the resultant vector R and the x-axis is φ. We can use trigonometry to find this angle.
tan(φ) = Ry / Rx
Finally, we can find the magnitude and angle of the resultant vector R using the equation:
R = sqrt(Rx^2 + Ry^2)
φ = arctan(Ry / Rx)
By substituting the known values and solving the equations, we can find the magnitude and angle of the resultant vector.