Given four non zero vectors `bar a,bar b,bar c and bar d`. The vectors `bar a,bar b and bar c` are coplanar but not collinear pair by pairand vector `bar d` is not coplanar with vectors `bar a,bar b and bar c and hat (bar a bar b) = hat (bar b bar c) = pi/3,(bar d bar b)=beta` ,If `(bar d bar c)=cos^-1(mcos beta+ncos alpha)` then `m-n` is :

Options

A. `cos^(-1)(cosbeta-cosalpha)`
B. `sin^(-1)(cosbeta-cosalpha)`
C. `sin^(-1)(sinbeta-sinalpha)`
D. `cos^(-1)(tanbeta-tanalpha)`

Answer

A