Equation of a line in 3D
In this post I will be talking about how to find vector equation of a line in 3D. To find vector equation of a line we need : A direction vector of the line Coordinates of any point on the line Equation from direction vector and a point on the line D irection or directional vector is a vector arrow parallel to the line. Some texts will use the term ‘Direction ratios’ or ‘Direction Numbers’ for direction vector. Direction numbers or direction ratios of a line is a set of three numbers that specify the direction of that line. A line with direction ratios of 1, 2, 3 basically means that \(\hat{i} + \hat{j} + \hat{k}\) is its direction vector, i.e. a vector parallel to that line. The procedure for finding the equation of a line is simple enough. Consider a line in 3D space; let’s name it L. Suppose \(\vec{d} = 3\hat{i} + 2\hat{j} - 8\hat{k}\) is its direction vector. Let P(5, 2, -4) be a point on L. Below is a rough picture of how everything is supposed t...