Vectors

The lines l₁ and l₂ have vector equations r = (-3, -1, 3) + λ(1, 2, -2) and r = (2, 2, 4) + μ(0, -2, -2) respectively, where λ and μ are real parameters. Determine whether l₁ and l₂ intersect, are parallel or are skew; if they intersect, find the coordinates of the point of intersection. [3]

The planes π₁ and π₂ have normal vectors (2, -2, 1) and (-2, -2, -1) respectively. Find the acute angle between π₁ and π₂. [2]

The plane π is given by r · (-1, 2, -2) = -5. The point P has coordinates (-3, 2, -2). By first determining the foot of perpendicular F from P to π, (a) find the position vector of F, [3] and (b) find the position vector of the reflection P' of P in π. [1]