### Cartesian Vector Components of Force FWhen a force \( F \) is expressed as a Cartesian vector, it is written as:\[ \mathbf{F} = F_x \mathbf{i} + F_y \mathbf{j} + F_z \mathbf{k} \]where \( \mathbf{i} \), \( \mathbf{j} \), and \( \mathbf{k} \) are unit vectors in the x, y, and z directions, respectively. #### Problem Statement:Given the force \( \mathbf{F} \) with a magnitude of 135 lb, the task is to find the nearest values of \( F_x \), \( F_y \), and \( F_z \). The diagram provided gives a visual representation of the force \( \mathbf{F} \) and the angles involved.#### Diagram Description:- There is a 3-dimensional coordinate system (\( x \), \( y \), and \( z \) axes).- Point \( A \) is where the force vector \( \mathbf{F} \) is applied.- The vector \( \mathbf{F} \) makes an angle of 70° with the horizontal projection \( AB \) and an angle of 30° with the vertical plane.- The horizontal projection \( AB \) extends 10 feet from the origin along the plane.- The base \( B \) is 5 feet along the x-axis and 7 feet along the y-axis from the origin.#### Possible Solution Choices:1. \( F_x = -70.5 \); \( F_y = 57.2 \); \( F_z = -83.2 \)2. \( F_x = 98.2 \); \( F_y = -44.7 \); \( F_z = -57.2 \)3. \( F_x = -70.4 \); \( F_y = 88.2 \); \( F_z = -59.4 \)4. \( F_x = 59.4 \); \( F_y = -88.2 \); \( F_z = -83.2 \)#### Calculation Methodology:To find the components \( F_x \), \( F_y \), and \( F_z \) of the force \( \mathbf{F} \), we can use trigonometric relationships from the angles provided. By projecting the force vector onto the coordinate axes and applying cosine and sine functions,

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Answered: If force F is expressed as a Cartesian…

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If force F is expressed as a Cartesian vector, it would be F = Fx i + Fy j + Fz k, where i, j, and k are unit vectors. Find the nearest Fx, Fy and Fz all in lb. 5 ft B 76 Z F = 135 lb 10 ft 70° 30° A y