Two vectors of magnitude 8 unit each are acting at a point making an angle120 degree with each other.determine the magnitude
use the law of cosines:
x^2 = 8^2 + 8^2 - 2*8*8*cos(60°)
or just take components up the middle
2 * 8 cos (120/2) = 16 cos 60 = 8
To determine the magnitude of the resultant vector formed by two vectors of equal magnitude and making an angle with each other, we can use the Law of Cosines.
If we have two vectors A and B of equal magnitude 8 units and an angle of 120 degrees between them, the formula for finding the magnitude of the resultant vector C is:
C^2 = A^2 + B^2 - 2AB*cos(theta)
where A and B are the magnitudes of the vectors, and theta is the angle between them.
Substituting the given values into the formula:
C^2 = 8^2 + 8^2 - 2(8)(8)*cos(120)
C^2 = 64 + 64 - 128*cos(120)
To evaluate cos(120), we need to convert the angle to radians since trigonometric functions generally work with radians. The formula to convert degrees to radians is:
radians = degrees * (pi / 180)
So, for cos(120):
cos(120) = cos(120 * (pi / 180))
Now, we can substitute the value for cos(120) and evaluate C:
C^2 = 64 + 64 - 128*cos(120)
C^2 = 64 + 64 - 128*cos(120 * (pi / 180))
C^2 = 64 + 64 - 128*(-0.5)
C^2 = 128 + 64
C^2 = 192
Taking the square root of both sides:
C = sqrt(192)
C ≈ 13.86 units (rounded to two decimal places)
Therefore, the magnitude of the resultant vector is approximately 13.86 units.