Coplanarity Using Determinant

Coplanarity Using Determinant

For vectors:

$$\vec a=a_1\hat i+a_2\hat j+a_3\hat k$$

$$\vec b=b_1\hat i+b_2\hat j+b_3\hat k$$

$$\vec c=c_1\hat i+c_2\hat j+c_3\hat k$$

the coplanarity condition is:

$$\begin{vmatrix}a_1&a_2&a_3\\b_1&b_2&b_3\\c_1&c_2&c_3\end{vmatrix}=0$$

Usage

- Used to check whether three vectors lie in the same plane.