-- Dot Product Learning Goal: To use the dot product to find the components of f
ID: 2845219 • Letter: #
Question
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Dot Product Learning Goal: To use the dot product to find the components of forces acting in arbitrary directions. A three-legged structure is shown below. It is attached to the around at points R = (4.50 0 Part A - Finding the Cartesian components of a force described by direction angles Find the Cartesian components of force P acting in the x, y. and z directions given P = 20.0 N. alpha = 115.0 degree. beta = 29.0 degree. and gamma = 76.3 degree. Recall that alpha is the angle between the vector and the x axis, , beta is the angle between the vector and the y axis, and gamma is the angle between the vector and the z axis. Express your answers, separated by commas, to three significant figures. Part B - Finding the angle between forces Find the angle between forces F and P Express your answer to three significant figures in degrees.Explanation / Answer
Let Px, Py, Pz be the components of P on x, y and z axes respectively.
Px = P*cos(alpha) = 20*cos(119) = -9.696 N
Py = P*cos(beta) = 20*cos(29) = 17.49 N
Pz = Pcos(gamma) = 20*cos(76.3) = 4.736 N
The components of F are not provided, so I can't find the angle between F and P. In general, if theta is the angle between two vectors,
theta = <vec1, vec2> / (abs(vec1)*abs(vec2))
Here, vec1 = F and vec2 = P, abs(.) denotes the vector magnitudes and <.> is the dot product.
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