The lines `bar r=bar a+tbar b ,barr=bar c+sbar d` coplanar if

The lines bar(r)=bar(a)+tbar(b),bar(r)=bar(c)+sbar(d) coplanar if

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 :

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 :

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 :

Find the point of intersection of the line bar(r)=2bar(a)+bar(b)+t(bar(b)-bar(c)) and the plane bar(r)=bar(a)+x(bar(b)+bar(c))+y(bar(a)+2bar(b)-bar(c)) where bar(a), bar(b), bar(c) are non coplanar vectors.

The point of intersection of the lines bar(r)=bar(a)+t(bar(b)+bar(c)), bar(r)=bar(b)+s(bar(c)+bar(a)) is

If the unit vectors bar(a),bar(b) and bar( c ) are coplanar then [2bar(a)-bar(b),2bar(b)-bar( c ),2bar( c )-bar(a)] = ……