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The sum of magnitudes of 2 forces acting at a point is 18 and magnitude of their resultant is 12.If the resultant is perpendicular with force of smaller magnitude what are magnitudes of forces? (ii)p+q=r(they are in vector form)p=q=r/root2 then find the angle between pair of vectors p,q and q,r and r,p |
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Answer» the two vectors. Let Q < P.Let the angle between the two vectors be Ф.Resultant of R = P² + Q² + 2 P Q COS Ф --- (1) We are given P + Q = 18, => Q = 18 - P. and, R = 12. Angle between R and Q = 90°.We have .So P² = R² + Q² - 2 R Q Cos 90° ----- (2) = R² + Q² - 0 = 12² + (18 - P)² = 144 + 324 + P² - 36 P => 36 P = 468 => P = 13 => Q = 18 - 13 = 5==========================Given R is perpendicular to Q. so angle is 90 deg.Use the equation (1) to find the angle Ф between P & Q, as MAGNITUDES of P, Q and R are known. The angle between R and P could be equal to (Ф - 90) deg. |
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