explain (A)linearly dependent and linearly independent (B) coplanar and non coplanar

the system of n vectors $x_1 ,x_2 , x_3 ,.........,x_n$  is said to be linearly dependent if there exist scalars $a_1 ,a_2 ,.......,a_n$ not all zero
such that
$a_1{x}_1 +a_2{x}_2 +a_3{x}_3 +.........+a_n{x}_n =0$
and the same set of vectors are said to be linearly independent if $a_1 = a_2 =a_3 =......=a_n=0$

if two vectors x and y are linearly dependent; $x=my where m\ne 0$

coplanar vectors:

four position vectors a, b , c and d are coplanar if and only if there exists four scalar x,y , z and w , not all zero such that
$$\begin{gathered} ax+by+cz+dw=0 \\ where x+y+z+w=0 \end{gathered}$$

if a, b and c are linearly independent then they are non coplanar vectors.


hope this helps you