question_answer

If a, b, c are the position vectors of three collinear points, then the existence of x, y, z is such that

A) \[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}=0,\,\,x+y+z\ne 0\]

B) \[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}\ne 0,\,\,x+y+z=0\]

C) \[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}\ne 0,\,\,x+y+z\ne 0\]

D) \[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}=0,\,\,x+y+z=0\]