Let L and Q be lines in R^3 given by the equations: Line L: (x y z)=(1 2 0)+t(2 -3 5) and line Q: (x y z)=(3 -13 13) +r(2 3 1). Are L and Q perpendicular? Justify your answer.

Answer 1

Two lines in R^3 are perpendicular if they intersect and meet at a right angle.

To show that they intersect you need to show that there is some number t such that

(1 2 0)+t(2 -3 5) =(3 -13 13) +t(2 3 1)

To show that they meet at a right angle you need to show their direction vectors have a dot product of zero. This is the same as showing (2 -3 5) & (2 3 1) have a dot product of zero.

Hope this helps.