How do you find the point of intersection of two vector lines?

Each vector line can be simplified into three separate equations in terms of the lines parameter and one of 'x,y and z.' This process can be done for both lines, creating six equations in total. By setting the values of x, y and z for these equations equal to one another, a value for both of the parameters can be found. These values can then be substituted back into the relevant vector equation to discover the point of intersection. Both parameter values should be substituted back in to ensure that the answer is the same for both lines, confirming your maths was correct.