\(l_1:\mathbf r=(1,-2,3)+\lambda(2,-1,a)\), \(l_2:\mathbf r=(-1,-1,-1)+\mu(3,-2,-2)\). The lines are perpendicular and intersect.

(a) Show a=4. [1]

(b) Find the position vector of the intersection. [4]

(c) Show A=(−5,1,−9) lies on l₁. [2]

(d) B is the reflection of A in l₂. Find its position vector. [2]