Find the resultant of two vectors of 3 units and 4 units acting at a point 0 at an angle of 45 degrees with each other using cosine role OC = R, find alpha
Using the cosine rule, we can find the magnitude of the resultant vector, R:
R^2 = 3^2 + 4^2 - 2*3*4*cos(45)
R^2 = 9 + 16 - 24cos(45)
R^2 = 25 - 24cos(45)
R^2 = 25 - 24*(sqrt(2)/2)
R^2 = 25 - 12sqrt(2)
R^2 ≈ 4.86
R ≈ 2.21
Therefore, the magnitude of the resultant vector is approximately 2.21 units.
Now, to find alpha (α), we can use the inverse cosine (arccos) function:
cos(α) = (3^2 + R^2 - 4^2) / (2*3*R)
cos(α) = (9 + 2.21^2 - 16) / (2*3*2.21)
cos(α) = (9 + 4.8841 - 16) / 13.26
cos(α) = -0.014 / 13.26
cos(α) ≈ -0.00106
α ≈ arccos(-0.00106) ≈ 90.31 degrees
Therefore, α is approximately 90.31 degrees.