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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
the answers are 13 and 5



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Let \vec{P}\ and\ Q be the two vectors.  Let Q < P.
Let the angle between the two vectors be Ф.

Resultant of \vec{P}\ and\ \vec{Q}:\ \ \vec{R}=\vec{P}+\vec{Q}

     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  \vec{P}=\vec{R}-\vec{Q} .
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.

2 3 2
sir you did not answer then find the angle between pair of vectors p,q and q,r and r,p
incomplete answer
plaese sir
if some equations are there, some part of the solution is worked out, the remaining can be done or not ? why do you want me to write the details.. is it your home work or mine ?
is it justified that you make the person answering your doubt to work more and you do not work at all ?
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