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 vec r* vec a =0 = vec r* vec b ,where vec a and vec b are non-coplanar vectors then

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

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 a, b and c are non-collinear unit vectors also b, c are non-collinear and 2atimes(btimesc)=b+c , then

What is the value of [vec a vec b vec c] if vec a, vec b, vec c are non-zero coplanar vectors ?

Show that the points A(3,2,1),B(4,5,5),C(4,2,-2) and D(6,5,-1) are coplanar.

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

If vec a , vec b and vec c are non-coplanar (independent) vectors, prove that the vectors vec a- 2 vec b+ 3 vec c , -2 vec a + 3 vec b- 4 vec c and vec a -vec b+ 2 vec c are also linearly independent.

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.