How Can the Sum of Vectors P and Q Exceed the Magnitude of Vector F?

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In the discussion, a force F with a magnitude of 12 N is analyzed alongside its components P and Q, which sum to 18 N. The confusion arises from the relationship between the magnitudes of P, Q, and F, as F is considered the resultant vector. It is clarified that P and Q can exceed the magnitude of F due to their directional components, particularly since Q is perpendicular to F. The "parallelogram law" is suggested as a geometric method to visualize the relationship between these vectors. Understanding this concept helps clarify how the sum of P and Q can indeed exceed the magnitude of the resultant vector F.
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A force F of magnitude 12 N, Please help!

A force F of magnitude 12 N has componenets P and Q. The sum of the magnitudes of P and Q is 18 N. The direction of Q is at right angles to F. Find the magnitude of Q.

I am not able to visualize the drawing. My question is this. I know the sum of two vectors is a third vector. So in the problem, it seems F is the third vector with a magnitude of 12 N. Then how can sum of P + Q = 18N. I am confused. Please help.
 
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Try to find an equivalent geometric problem, by applying the "parallelogram law" for adding vectors. P and Q will be the sides of the parallelogram and F will be the diagonal.
 

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