The lines l1 and l2, defined by the equations r=(4+t)i + (a+3t)j + (2-3t)k and r=(1-2s)i + (1-s)j + (1+s)k, intersect at a specific point. To find the value of a, equate the i, j, and k components of both lines, resulting in a system of equations. By solving the i and j equations for parameters t and s, and substituting these values into the k equation, the value of a can be determined definitively.
PREREQUISITESStudents and professionals in mathematics, physics, and engineering who are working with vector equations and need to understand line intersections in three-dimensional space.
Punch said:The equation of the lines l1 and l2 are are r=(4+t)i + (a+3t)j + (2-3t)k and r=(1-2s)i + (1-s)j + (1+s)k respectively, where t and s are real parameters. It is given that the lines intersect. Find the value of a.