Two forces P and Q act at a point and produce a resultant R1. If force P is reversed in direction (replaced by -P), the new resultant R2 is found to be perpendicular to R1. What is the relationship between the magnitudes of P and Q?

P = Q
P = 2*Q
P = Q/2
P = sqrt(2)*Q

Correct answer: P = Q

Solution

The original resultant R1 = P + Q and the new resultant R2 = -P + Q. For these to be perpendicular, their dot product must be zero: (P+Q).(-P+Q) = |Q|² - |P|² = 0, which gives |P| = |Q|.

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