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

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The discussion centers on the vector problem involving a force F with a magnitude of 12 N, and two components P and Q, where the sum of their magnitudes equals 18 N. The direction of vector Q is perpendicular to vector F. By applying the parallelogram law of vector addition, it is established that the resultant vector F, which is the diagonal of the parallelogram formed by P and Q, cannot exceed the sum of P and Q. Therefore, the magnitude of Q can be calculated using trigonometric relationships, confirming that the scenario is geometrically valid.

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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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