To understand Cartesian representations of vectors and how they can be determine

Question

To understand Cartesian representations of vectors and how they can be determined from direction and magnitude: to learn how to represent vectors expressed as a product of the component magnitude and the unit direction vectors i, j, and k: and to learn how to represent a vector component as a function of the angle between the vector and the coordinate axis. As shown, a pole is subjected to three forces: F, P, and T. The force F expressed in Cartesian vector form is F = [8i + 7j + 10 k] N. Force P has magnitude 9.00 N and acts in the direction given by these direction angles: alpha = 132 degree, beta = 48.2 degree, and gamma = 70.5 degree to the x, y, and z axes respectively. Force T lies within the yz plane, its direction is given by the 3-4-5 triangle shown, and its magnitude is 20 N. Calculating the magnitude of a vector from its components What is the magnitude of F? Express your answer to three significant figures and include the appropriate units. F= 14.6 N Components of a vector Determine the components of P in the i, j, and k directions. Express your answers, separated by commas, to three significant figures. P_z, P_y, P_z = -6.02, 6.00, 3.00 N, N, N Finding Cartesian components from right triangles What are the Cartesian components of force T? Express your answers, separated by commas, to three significant figures. T = 0, 8.76, 11.7

Explanation / Answer

Since T lie in yz plane

and It form base as 3 and height as 4 and hypoteneus as 5

angle let A is formed with base y and hypoteneuse

tanA = 4/3

A = 53.13

Since it s lying in yz

x component = 0

y compnent = - 20 cos(53.13) = -12.008

z component = 20 sin(53.13) = 16.000

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