A force F_1 = A hat{j} is applied to a point | vedclass

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(A) Given that,$F_1 = A \hat{j}, r_1 = a \hat{i}$$F_2 = B \hat{i}, r_2 = b \hat{j}$The moment of force (torque) is given by $	au = r 	imes F$.For th

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$(a A - b B) \hat{k}$

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(A) Given that,$F_1 = A \hat{j}, r_1 = a \hat{i}$$F_2 = B \hat{i}, r_2 = b \hat{j}$The moment of force (torque) is given by $	au = r 	imes F$.For the first force:$	au_1 = r_1 	imes F_1 = (a \hat{i}) 	imes (A \hat{j}) = a A (\hat{i} 	imes \hat{j}) = a A \hat{k}$For the second force:$	au_2 = r_2 	imes F_2 = (b \hat{j}) 	imes (B \hat{i}) = b B (\hat{j} 	imes \hat{i}) = b B (-\hat{k}) = -b B \hat{k}$The net moment relative to $O$ is:$	au = 	au_1 + 	au_2 = a A \hat{k} - b B \hat{k} = (a A - b B) \hat{k}$

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