Direction Angle Calculation of Force Q

What is the direction angle between Force Q and the X-coordinate axis?

A) 35.69

B) 56.93

C) 78.69

D) 33.83

E) 53.96

Answer:

The direction angle between Force Q and the X-coordinate axis is approximately 56.93 degrees.

To find the direction angle between Force Q and the X-coordinate axis, we need to calculate the angle formed between the force vector and the positive X-axis.

Given that the force vector is directed from point C(-3,4,0) to point D(1,5,3) and has a magnitude of 450N, we can calculate the components of the force vector in the X, Y, and Z directions:

F_x = 1 - (-3) = 4

F_y = 5 - 4 = 1

F_z = 3 - 0 = 3

Next, we can use the formula: θ = arccos(F_x/|F|) to calculate the angle, where |F| is the magnitude of the force vector (450N).

By plugging in the values, we get: θ ≈ 56.93 degrees

Understanding how to calculate direction angles is crucial for analyzing and solving vector-related problems in engineering and physics.