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?

Question

Nigel · Answer

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.

Determining the Direction Angle of Force Q

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