IIT JEE , AIEEE Forum - Physics , Mechanics

kghedriu

well...let us assume the vectors to be F1 and 8-F1....now let us assume that F1 is the smaller vector......

for convenience i ll represent F1 by u and 8-F1 by v.....

now,

u^2+v^2+2uvcos

= 16 (formula for the resultant)

so

(u+v)^2+ 2uv+2uv cos

= 16

so, u+v=8 (given)...substituting...

48= 2uv(1-cos

)-------------------------(1)

now, angle made by the resultant is given as:

Tan

= v sin

/u+v cos

...and sice angle is 90 deg, it implies...

tan90 = infinity.....

therefore u+v cos

=0

.: cos

= -u/v-----------------------------(2)

substituting in equation (1)....we get....

48= 2uv(1-u/v)

now, put v=8-u....

u get 24= 8u...

.: u=3, hence V=5...

.: angle btween them = cos^-1(-3/5) (cos inverse of -3/5)

hope m clear..

thank u..

Goutham.K