The magnitude of a moment about a line segment connecting points P and Q due to...

 

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The magnitude of a moment about a line segment connecting points P and Q due to a force F applied at point R (with R not on the line through P and Q) can be calculated using the scalar triple product, Part A - Finding the scalar triple product Which of the following equations correctly evaluates the scalar triple product of three Cartesian vectors R, S, and T? MPQ = uPQ · rx F, • View Available Hint(s) where r is a position vector from any point on the line through P and Q to Rand upo is the O R.Sx T R (S,T:- ST,)+ R(S T:- S T.) +R:(S,T,-S,T.) unit vector in the direction of line segment PQ. The unit vector upo is then multiplied by this magnitude to find the vector representation of O R Sx T = R,(S,T. - S.T,) i +R,(S T: - ST)j+R:(S,T,- SyT;) k the moment. O R.Sx T = R (S,T: – ST,) i- R,(S.T:- ST) j+ R:(S.T,- S,T) k O R.SxT = R (S,T: - ST,) – R,(S T: - S.T.)+ R:(S T,- S,T.) As shown in the figure, the member is anchored at A and section AB lies in the x-y plane. The dimensions are a1 = 1.6 m, y1 = 1.7 m, and z1 = 1.6 m. The force applied at point C is F = [-185 i+ 80 j+ 190 k) N. Submit (Figure 1) Part B - Calculating the moment about AB using the position vector AC Using the position vector from A to C, calculate the moment about segment AB due to force F. Figure 1 of 1 Express the individual components to three significant figures, if necessary, separated by commas. • View Available Hint(s) F ΑΣφ vec MAB =[ i, j, k] N. m B Submit Part C - Calculating the moment about AB using the position vector BC Using the position vector from B to C, calculate the moment about segment AB due to force F. Express the individual components to three significant figures, if necessary, separated by commas. The magnitude of a moment about a line segment connecting points P and Q due to a force F applied at point R (with R not on the line through P and Q) can be calculated using the scalar triple product, Part A - Finding the scalar triple product Which of the following equations correctly evaluates the scalar triple product of three Cartesian vectors R, S, and T? MPQ = uPQ · rx F, • View Available Hint(s) where r is a position vector from any point on the line through P and Q to Rand upo is the O R.Sx T R (S,T:- ST,)+ R(S T:- S T.) +R:(S,T,-S,T.) unit vector in the direction of line segment PQ. The unit vector upo is then multiplied by this magnitude to find the vector representation of O R Sx T = R,(S,T. - S.T,) i +R,(S T: - ST)j+R:(S,T,- SyT;) k the moment. O R.Sx T = R (S,T: – ST,) i- R,(S.T:- ST) j+ R:(S.T,- S,T) k O R.SxT = R (S,T: - ST,) – R,(S T: - S.T.)+ R:(S T,- S,T.) As shown in the figure, the member is anchored at A and section AB lies in the x-y plane. The dimensions are a1 = 1.6 m, y1 = 1.7 m, and z1 = 1.6 m. The force applied at point C is F = [-185 i+ 80 j+ 190 k) N. Submit (Figure 1) Part B - Calculating the moment about AB using the position vector AC Using the position vector from A to C, calculate the moment about segment AB due to force F. Figure 1 of 1 Express the individual components to three significant figures, if necessary, separated by commas. • View Available Hint(s) F ΑΣφ vec MAB =[ i, j, k] N. m B Submit Part C - Calculating the moment about AB using the position vector BC Using the position vector from B to C, calculate the moment about segment AB due to force F. Express the individual components to three significant figures, if necessary, separated by commas.

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Find the scalar triple product of RSXT Let RRiR jRk SS i ... View the full answer