When the vector sum of three co-planar forces, , and , is parallel to , we can conclude that and
A) must sum to zero.
B) must be equal and opposite.
C) must have equal and opposite components perpendicular to .
D) must have equal and opposite components parallel to .
E) must have equal and opposite components parallel and perpendicular to .

Question

When the vector sum of three co-planar forces,  ,  and  , is parallel to  , we can conclude that  and 
A) must sum to zero. 
B) must be equal and opposite. 
C) must have equal and opposite components perpendicular to . 
D) must have equal and opposite components parallel to . 
E) must have equal and opposite components parallel and perpendicular to .

Quizplus · Accepted Answer

If the vector sum of three co-planar forces is parallel to a vector, it means that the forces have a common component in the direction of that vector. Therefore, the component of forces 11eb6adc_ed60_1afa_b0cf_c79a3cf7c03a_TB8245_11 and 11eb6adc_ed60_420b_b0cf_0bc35dfdea1a_TB8245_11 perpendicular to 11eb6adc_ed60_691c_b0cf_b7f1fbdea7d9_TB8245_11 must cancel out the common component of the three forces parallel to 11eb6adc_ed60_1af9_b0cf_53b501c1e03b_TB8245_11. This means that both forces must have equal and opposite components perpendicular to 11eb6adc_ed60_691c_b0cf_b7f1fbdea7d9_TB8245_11 (Choice C). It is not necessary for the forces to have equal and opposite components parallel to 11eb6adc_ed60_691d_b0cf_03308a03f7b4_TB8245_11 or equal and opposite components parallel and perpendicular to 11eb6adc_ed60_902e_b0cf_733e80e793b1_TB8245_11, so Choices D and E are incorrect. Choice A is incorrect because the forces do not have to sum to zero in order to have a vector sum parallel to another vector. Choice B is incorrect because the forces do not have to be equal in magnitude in order to have a vector sum parallel to another vector.

When the Vector Sum of Three Co-Planar Forces