As shown in the figure A 0 0 6 B 2 3 0 C 3 2 0 represent thr

As shown in the figure A (0, 0, 6), B (2, -3, 0), C (3, 2, 0) represent three points in three-dimensional Coordinate system on a flag pole. If F_B = 560 N and F_C = 700 N, express both the forces in Cartesian vector form 25 points

Solution

Answer -

Since the coordinates of Points A, B and C are (0,0,6), (2,-3,0) and (3,2,0) in the three dimensions on a flag pole and the values of Force along B and C are;

F_B = 560 N, F_C = 700 N.

The values of F_B along three points can be given as;

Along A Point = 560*0 x +560*0 y +560*6 k = 3360 k

Along B Point = 560*2 x - 560*3 y +560*0 k = 1120 x - 1680 y

Along C Point = 560*3 x +560*2 y +560*0 k = 1680 x +1120 y

Thus, the value of F_B in cartesian vector form;

F_B = 3360 k +1120 x -1680 y +1680 x +1120 y = 2800x - 560y + 3360k

Now, The values of F_C along three points can be given as;

Along A Point = 700*0 x +700*0 y +700*6 k = 4200 k

Along B Point = 700*2 x - 700*3 y +700*0 k = 1400 x - 2100 y

Along C Point = 700*3 x +700*2 y +700*0 k = 2100 x +1400 y

Thus, the value of F_C in cartesian vector form;

F_B = 4200 k +1400 x -2100 y +2100 x +1400 y = 3500x - 700y + 4200k