To understand Cartesian representation of vectors and how they can be determined

Question

To understand Cartesian representation 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 + 9j + 10k| N. Force P has magnitude 8.31 N and acts in the direction given by these direction angles: alpha = 104 degree, beta = 15.7 degree and gamma = 83.1 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 12 N. Components of a vector Determine the components of P in the i, j, and k directions. Finding Cartesian components from right angle triangles What are the Cartesian components of force T? Express your answers, separately by commas, to three significant figures.

Explanation / Answer

The x component will be zero since in the yz pane.

The y component will be -7.22 and the z component will be 9.58 using trigonometric relations.

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