Hello, kandyfloss!

The vector equations can be written:Lines and have vector equations: .

Show that and intersect and find the position vector of the point of intersection.

. . . .

From [9], we have: .

Substitute into [8]: .

Substitute into [1], [2] and [3]:

. .

Substitute into [4], [5] and [6]:

. .

Therefore, the lines intersect at: .

The position vector of is: .