Like in the two-dimensional plane, we need a slope and a point through which the line passes, in a three-dimensional plane, a point through which the line passes is needed, along with a direction vector to entail the direction of the line. In two-dimensional geometry, the slope gives the depth or height of the line. Similarly, in three-dimensional geometry, the idea of the direction of the line whose equation has to be derived is given by the direction vector.The formula to find the equation passing through two points in 3d is \\[ \\frac{x - x_{1}}{l} = \\frac{y - y_{1}}{m} = \\frac{z - z_{1}}{n}\\], where the direction vector is (l, m, n) and the point through which the line is passing is \\[(x_{1}, y_{1}, z_{1})\\].