Vector magnitude

Jul 2018
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Two forces, each equal to P, act at right angles. Their effect may be neutralized by a third force acting along their bisector in the opposite direction with a magnitude of___________
in this diagram, the resultant vector is the opposite direction, So what should I do the addition of vector or subtraction of vector? I am confused.
 

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Aug 2010
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Two forces, each equal to P, act at right angles. Their effect may be neutralized by a third force acting along their bisector in the opposite direction with a magnitude of___________
in this diagram, the resultant vector is the opposite direction, So what should I do the addition of vector or subtraction of vector? I am confused.
You certainly want to add the two given vectors, That is what the "effect" or two vectors means! Calling this "third vector" Q, We have P+ P+ Q= 0 (that's what "neutralized" means) so Q= -2P.

We can, without loss of generality, take the x and y axes in the directions of the two vectors. Then you can write the two vectors as <P, 0> and <0, P>. They sum to <P, P> which has magnitude $P\sqrt{2}$. The "third force" is the opposite of that <-P, -P> which also has magnitude $P\sqrt{2}$.
 
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