Question

if an angle between two vectors of equal magnitude P is theta ,the magnitude of the difference of the vectors is

Answer 1

Now we have a simple triangle to solve. Use cosine law to determine the magnitude of the resultant:

R2=A2+A2−2(A)(A)cos(180−θ)R2=A2+A2−2(A)(A)cos(180−θ)

but cos(180−θ)=−cosθcos(180−θ)=−cosθ

∴∴ R2=A2+A2−2(A)(A)(−cosθ)R2=A2+A2−2(A)(A)(−cosθ)

or

R2=A2+A2+2(A)(A)cosθR2=A2+A2+2(A)(A)cosθ

R2=2A2+2(A2)cosθR2=2A2+2(A2)cosθ

R2=2A2(1+cosθ)R2=2A2(1+cosθ)

R=A2(1+cosθ)−−−−−−−−−√