Condition for Collinearity of 3 Points

1. Three Points \(A\), \(B\) and \(C\) having Position Vectors \(\vec{A}\), \(\vec{B}\) and \(\vec{C}\) respectively are Collinear if:
   1. \(\vec{AB} \times \vec{AC}=0\)   (Applicable for Points in 2D and 3D only)
   2. \(\frac{|\vec{AB} \cdot \vec{AC}|}{|\vec{AB}||\vec{AC}|}=1\)   (Applicable for Points in 2D,3D and Higher Dimensions)
   where \(\vec{AB}=\vec{A}-\vec{B}\), \(\vec{AC}=\vec{A}-\vec{C}\)
2. In 2D only, 3 points (\(x_1,y_1\)), (\(x_2,y_2\)) and (\(x_3,y_3\)) are Collinear if:
   
   \(\begin{vmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \end{vmatrix}=\begin{vmatrix} x_1-x_2 & y_1-y_2 \\ x_1-x_3 & y_1-y_3\end{vmatrix}=0\)