The lines and 12 have equations r = 8i + 2j + 3k + 2(1 – 2j) and r = 5i + 3j – 14k + 12(2j – 3k) respectively. The point P on It and the point Q on I2 are such that PQ is perpendicular to both I1 and I2. Find the position vector of the point P and the position vector of the point Q.
The points with position vectors 8i + 2j + 3k and 5i + 3j – 14k are denoted by A and B respectively.
i. A̅P̅(vector) × A̅Q̅(vector) and hence the area of the triangle APQ,
ii. The volume of the tetrahedron APQB. (You are given that the volume of a tetrahedron is 1/3 x area of base x perpendicular height)