Question

at what angle the two forces f1+f2 and f1-f2 act so that the resultant is {2(f1^2+f2^2)}^1/2?

Answer 1

if R1 and R2 are given two vectors then resultant of these vectors
R=√(R1^2+R2^2+2R1.R2cos@)
where @ is angle between vectors
use this ,
[2(f1^2+f2^2]^1/2=[(f1-f2)^2+(f1+f2)^2+2(f1-f2)(f1+f2)cos@]^1/2

squaring both side ,
2(f1^2+f2^2)=2(f1^2+f2^2)+2(f1^2-f2^2)cos@

cos@=0
hence @=π/2
hence angle between them π 2