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

Show that points with position vectors a-2b+3c,-2a+3b-c and 4a-7b+7c are collinear. It is given that vectors a,b and c and non-coplanar.

Show that the points P(a+2b+c),Q(a-b-c),R(3a+b+2c) and S(5a+3b+5c) are coplanar given that a,b and c are non-coplanar.

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

Show that the vectors vec(a),vec(b) and vec( c ) coplanar if vec(a)+vec(b),vec(b)+vec( c ) and vec( c )+vec(a) are coplanar.

Given three vectors veca, vecb and vecc are non-zero and non-coplanar vectors. Then which of the following are coplanar.

If the unit bar(a),bar(b) and bar( c ) are coplanar then …………..

a and b are non-collinear vectors. If c=(x-2) a+b and d=(2x+1)a-b are collinear vectors, then the value of x= . . .

Consider the set of eight vector V={a hat i+b hat j+c hat k ; a ,bc in {-1,1}}dot Three non-coplanar vectors can be chosen from V is 2^p ways. Then p 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)] = ……

Statement-I If the vectors a and c are non collinear then the lines r=6a-c+lambda(2c-a) and r=a-c+mu(a+3c) are coplanar. Statement-II There exist lambda and mu such that the two values of r in Statement-I becomes same.