# The resultant of p vector and q vector is r vector. When the direction of q vector is reverse then the resultant is s vector . Prove that sq of r+sq of s =2(sq of p+sq of q)

Arun
25750 Points
6 years ago
Please draw a parallelogram AB CD.  Let CD be parallel to AB. Let BC be parallel to AD.  Let vector P be represented by AB. Let Q be represented by AD.  Now the resultant force of P & Q is given by parallelo gram law as
R =  square root [ P²+ Q² + 2 P Q cos A ]  = This is diagonal AC
If the angle is reversed, That is, reverse vector AD or Q. Now draw parallelogram AEFB so that AE = - Q = - AD.   FB = EA.  Now the diagonal  AF will be parallel to diagonal BD.  The angle at A in AEFB is  180 - A.  SO its cosine is - Cos A.
S = squareroot [ P² + Q² - 2 P Q cos A ]
So R² + Q² = 2 [P² + Q² ]
as the other terms cancel.
This is also a relation between sides of a parallelogram and diagonals
Avika
15 Points
5 years ago
R=
2086 Points
5 years ago
the best method to solve this is as follows:
p+q= r
and p – q= s
taking magnitude and squaring
p^2 + q^2 + 2p.q= r^2
p^2 + q^2 – 2p.q= s^2