If vector a, vector b, vector c are three non-zero vectors, no two of which are collinear and the vector a + vector b

Question

If  \(\vec a,\,\vec b, \,\vec c \) are three non-zero vectors, no two of which are collinear and the  \(\vec a+\vec b\)  is collinear with  \(\vec c,\,\vec b+\vec c\)  is collinear with  \(\vec a\), then  \(\vec a+\vec b + \vec c\)

A. \(\vec a\)

B. \(\vec b\)

C. \(\vec c\)

D. none of these

Answer 1

Correct option is D. none of these

As  \(\vec a+\vec b\) is collinear with  \(\vec c\).

As  \(\vec b+\vec c\) is collinear with  \(\vec a\).

Adding  \(\vec c\) both sides of the equation (i)

Adding  \(\vec a\) both sides of the equation (iii),

Equating the RHS of equation (iii)& (iv), being their LHS equal,

As, a is not collinear with c,