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 pie is subjected to three forces: F, P, and T The Force F expressed in Cartesian vector form is F - [5 i + 8 j 10 k N Force P has magnitude 8.19 N and acts in the direct on given by these direction angles: a - 111 Beta - 31.3^12 and lambda - 68.5 to the x y. and 2 axes respectively Force T test within the yz pane its direction is given by the % 4 5 triangle Sown. and Is magnitude is 10 N What is the magnitude or F? Express your answer to three significant figures and include the appropriate units. Part B - Components of a vector Detaining the components of P in the i, j, and direction. Express your answers, separated by commas, to three significant figures. Finding Cartesian components from right triangles What are the Cartesian components of force T? Express your answers, separated by commas, to three significant figures.

Explanation / Answer

Given: F=[5i+8j+10k]N, P = 8.19N, T = 10N

A) Magnitude of F = Sqrt(52+82+102) = 13.74773 N

B) P = 8.19*cos(111) i + 8.19*cos(31.3) j + 8.19*cos(68.5) k

Therefore, P = -4.11584 i + 8.135029 j + 6.6892 k

C) T = -10*cos(3/5) j + 10*sin(3/5) k

T = -8.25336 j + 5.64643 k

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