Express force F as a Cartesian vector Express your answer in

Express force F as a Cartesian vector. Express your answer in terms of the unit vectors I, j, and k. Use the \'vec\' button to denote vectors in your answer. Express your answer using three significant figures. F =___lb Determining the coordination direction angle alpha F. Express your answer to three significant figures and include the appropriate units. Alpha =___Determine the coordinate angle beta of F. Express your answer using three significant figures. beta =___Determine the coordination direction of gamma of F. Express your answer using three significant figures. gamma =___

Solution

B = (5, -7, 0) ft

Az = 10 sin70 = 9.40 ft

Ay = 9.40 cos30 = 8.14 ft

Ax = - 9.40 sin30 = -4.7 ft

A = (-4.7, 8.14, 9.40) ft

F is along AB vector.

AB vector = B - A = 9.7 i - 15.14j - 9.40 k

AB = sqrt(9.7^2 + 15.14^2 + 9.40^2) = 20.29

Direction vector, ABcap = vector AB / AB

  
Vector F = |F| ABcap

= 135 ( 9.7 i - 15.14j - 9.40 k ) / 20.29

= 64.54i - 100.74j - 62.54 k lb ,,,,,,,,,,,Ans

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(B) alpha = cos^-1(Fx / F) =cos^-1(64.54 / 135) =61.44 deg

(C) beta = cos^-1(Fy /F) = cos^-1(-100.74/135) = 138.26 deg

(D) gamma = cos^-1(Fx/F) = 117.6 deg