If a,b and c are coplanar show `"[a+b b+c c+a]"` are coplanar.

Show that the vectors a-2b+4c,-2a+3b-6c and -b+2c are coplanar vector, where a,b,c are non-coplanar vectors.

If a, b and c are three coplanar vectors. If a is not parallel to b, show that c=(|[c*a, a*b], [c*b, b*b]|a+|[a*a, c*a], [a*b, c*b]|b)/(|[a*a, a*b], [a*b, b*b]|) .

If a, b and c are non-coplanar vectors and d=lambda vec a+mu vec b+nu vec c , then lambda is equal to

If a,b and c are non-coplanar vectors, prove that 3a-7b-4c, 3a-2b+c and a+b+2c are coplanar.

If a +b+c = alphad, b+c+d=beta a and a, b, c are non-coplanar, then the sum of a +b+c+d =

For any three vectors vec a,vec b and vec c , show that vec a- vec b,vec b- vec c and vec c- vec a are coplanar.

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 :

If a,b,c, d are in G.P., show that : a+b,b+ c and c+d are also in G.P.

Show that vectors vec a ,\ vec b ,\ vec c are coplanar if vec a+ vec b ,\ vec b+ vec c ,\ vec c+ vec a are coplanar.

If the vectors vec a, vec b, vec c are coplanar then (vec a xx vec b)* vec c = (vec b xx vec c)*vec a =...........