Determining the Direction Angle of Force Q

What is the direction angle between force Q of magnitude 450N, directed from point C(-3, 4, 0) to D(1, 5, 3), and the z-coordinate axis?

To determine the direction angle between force Q and the z-coordinate axis, we need to consider the z-component of the force vector. The direction angle is the angle between the force vector and the positive z-direction. First, we find the z-component of the force vector Q by subtracting the z-coordinate of point C (0) from the z-coordinate of point D (3). This value gives us the displacement in the z-direction as we move from point C to point D. Next, we calculate the magnitude of force Q using the Pythagorean theorem, which involves the x, y, and z components of the force vector. Finally, we find the direction angle using trigonometric functions, where the direction angle θ = arctan(z-component/magnitude of Q). Understanding the direction angles of forces is crucial in engineering and physics, especially when analyzing forces in three-dimensional systems. The direction angle provides valuable information about the orientation of forces in space, aiding in the design and analysis of various structures and mechanisms.

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