# Vectors

#### Punch

##### New member
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

##### Well-known member
MHB Math Helper
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

##### Well-known member
MHB Math Helper
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.