Triangle law in forces

Question

Triangle law gives us the magnitude and direction of two forces acting at a point. To calculate the resultant force, we complete the triangle, but in case of forces, won't the vertical component being moved to the tail of horizontal component give us another force because that might result in a force that produces torque. Then, how can I know the resultant vector of the forces following triangle law of vector.

How do I move vector B(in the right) to the tail of A(the left diagram) because won't this mean that the force is acting at some other point?

Answer 1

You are correct that you can't move vector B as such. Your correct schematic is what is shown on the right. This shows the point of origin of the vectors as well as of the new resultant vector C.

But in order to calculate the magnitude and direction of this new vector C, we don't have to worry about point of origin. If magnitude and direction is all, then you can rearrange them as you wish and thereby reach the traingle of your left sketch. This is indeed a sketch that does not show the correct origins of the forces - it just let's you calculate the magnitudes and angles with trigonometry.

Since you know the correct point of origin already, there is no problem in you doing this on-the-side sketch and calculation to find magnitude and direction. Then you can apply it to vector C from the correct starting point afterwards.

Answer 2

Actually, the point where a force is being applied doesn't depends on the starting point (or the ending point) of a vector line. We draw vector lines to understand the magnitude and the direction of the vector quantity. The arrow in the vector line means the direction and the length of the line means the magnitude (the magnitude of a vector quantity is proportional to the length of the vector line.) Thats all.

So in your figure it won't produce any torque by the mean you said (Yes, can produce by any other mean.) Because it is done by the Parallel Theorem. So moving a vector doesn't means that the vector is acting in any other point.