The equations of the plane π, and the lines L1 and l2 are given by
π: tx-2y+z=13
L1: r = (2i + j + 3k) + λ [2t i + (t² – 1) j – 2k]
L2: x – 4 = y, z = 5
where t and λ are real constants.
(a) Given that the shortest distance from the point P with coordinates (3, 3, -5) to π is 6, find the possible values of t.
(b) Show that L1 is parallel to π, and find a condition on t such that L1 is not on π.
For the case where t=2,
(i) show that L2 lies on π
(ii) given that A is a point on L1, and B is a point on L2, find the position vectors of A and B such that AB is perpendicular to both L1 and L2.
(iii) find the vector equation of the line of reflection of L1 in π.
