# 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

1
by rajusetu
the answers are 13 and 5

2015-04-05T11:03:17+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Let be 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.

sir you did not answer then find the angle between pair of vectors p,q and q,r and r,p