Question 4

Skew lines are a pair of lines that are non-intersecting, non-parallel, and non-coplanar. This

implies that skew lines can never intersect and are not parallel to each other. Given two lines

(a)

(b)

(c)

[]-1

=

4₁:

3 + t 1 and L₂:

Prove that L₁ and L₂ are skew lines.

Find a vector that connects these two lines.

=+₁₂₁

+ t 0

(6 marks)

(3 marks)

Plane ß lies exactly halfway between the two lines and intersects neither. Use the results

in Question 4(b) to find the Cartesian and vector equation of plane ß.

(16 marks)