Question

At what angle do the forces (P+Q) and (P-Q) act so that the resultant is :
$\sqrt{2 {p}^{2} + {q}^{2} }$



$\sqrt{3p^{2} + q^{2} }$

Answer 1

hola;;;;

#.....if A and B are two vectors at angle theta then there resultant vector has magnitde R given by 
R.R=(A.A+B.B+2AB cos theta) 
here in your question A=P+Q and B=P-Q and R.R= 3P.P+Q.Q let the angle between them be theta. 
thus 
3P.P+Q.Q=(P+Q).(P+Q) +(P-Q).(P-Q) +2(P+Q)(P-Q) cos theta 
LHS=(P.P+Q.Q+2PQ) +(P.P+Q.Q-2P.Q)+2(P.P-Q.Q) cos theta 
3P.P+Q.Q=2P.P+2Q.Q+2(P.P-Q.Q) cos theta 
P.P-Q.Q=2(P.P-Q.Q) cos theta 
cos theta =1/2 
cos theta =cos 60 
theta = 60 .....#

tysm.................@kundan

Answer 2

Answer:

Answer is given above.