when two forces of magnitude p and q are perpendicular to each other their resultant east of the magnitude are when they are at the angle of 180 to each other their resultant is offline attitude are by root 2 find the ratio of p and q
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R² = P² + Q² + 2PQ cos 90°
R² = P² +Q²
Now
R²/2 = P² + Q² -2PQ
P-Q = R/sqrt(2) ......(i)
R² /2 = R² - 2PQ
R² = 4PQ
(P+Q)² = P² + Q² + 2PQ = R² + R²/2
P+Q = sqrt3 * R/sqrt (2) .....(ii)
Solve equation 1 and 2
And then find P and Q , then you will be able to find the ratio.
Hope this will help you
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