A 26-lb. force vector that makes an angle of 101° counterclockwise from the -y direction. Determine the x and y components of the following three vectors in the xy plane.
"Determine the x and y components of the following three vectors in the xy plane."
Did you give us the full question? Is there more to it, like an image or something that we didn't get?
To determine the x and y components of a vector, we can use trigonometry. Given that the force vector makes an angle of 101° counterclockwise from the -y direction, we can consider this as an angle measured from the positive x-axis in the counterclockwise direction.
First, let's determine the value of the angle between the force vector and the positive x-axis. Since the force vector is counterclockwise from the -y direction, the angle between it and the positive x-axis will be 90° minus 101°, which is -11°.
Now, we can use this angle to determine the x and y components of the vector. The x component (F_x) can be calculated using the formula F_x = F * cos(θ), where F represents the magnitude of the force vector and θ represents the angle in radians.
F_x = 26 lbs * cos(-11°)
F_x = 26 lbs * cos(-0.1919)
F_x ≈ 26 lbs * 0.9828
F_x ≈ 25.5396 lbs
Similarly, the y component (F_y) can be calculated using the formula F_y = F * sin(θ).
F_y = 26 lbs * sin(-11°)
F_y = 26 lbs * sin(-0.1919)
F_y ≈ 26 lbs * (-0.9847)
F_y ≈ -25.5612 lbs
Therefore, the x component of the vector is approximately 25.5396 lbs and the y component is approximately -25.5612 lbs.