MHB It is given that the lines intersect. Find the value of a.

[Punch]

^{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.}

 

[Prove It]

^{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.}

Since the lines intersect, there must be some point where the i, j and k components are all equal. So set them equal to each other and try to solve the system.

 

[HallsofIvy]

Notice that you will have three equations in only two variables. Solve the i and j equations for r and t, then put those values into the k equation to determine a.