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 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 the points P(vec a + 2 vec b + vec c), Q (2 vec a + 3 vec b), R(vec b + t vec c) are collinear, where vec a, vec b, vec c are three non-coplanar vectors, the value of t is

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

The vectors vec a + vec b + vec c, 2 vec a+ vec b + 3 vec c and vec a + 2 vec b + 3 vec c , where vec a, vec b , and vec c are non coplanar vectors , are

If 1/a,1/b,1/c are in A.P and a,b -2c, are in G.P where a,b,c are non-zero then

If veca, vecb, vecc are non-coplanar vectors and lamda is a real number, then the vectors veca + 2 vecb + 3 vec c , lamda vecb + mu vec c and (2 lamda -1) vecc ar non-coplanar for:

Show that the points A(-1,4,-3), B(3,2,-5) C(- 3,8,-5) and D (-3,2,1) are coplanar

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

The unit vector which is orthogonal to the vector vec a = 3i+2j+6k and is coplanar with the vectors vec b = 2i+j+k and vec c = i-j+k is

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