Question 9
Referred to the origin O, the points A(4,1,3), B(-2,7,6) and
C(1,1,4) have position vectors \(a\), \(b\) and \(c\) respectively.
(i) Find the vector \((b - a) \times (c - a)\).
(ii) Hence, or otherwise, find the equation of the plane
ABC. Express your answer in the form \(r \cdot n = d\).
(iii) The point D with coordinates (5, -3, \lambda) lies in the
plane ABC. Find the value of \(\lambda\).
(iv) Prove that ABCD is a trapezium and find its area.