The points A,B and C have position vectors , relative to the origin O given by ## OA= i+2j+3k, OB=4j+k , OC=2i+5j-k.## A fourth point D is such that the quadrilateral ABCD is a parallelogram.
i) Find the position vector of D and verify that the parallelogram is a Rhombus.
ii)The plane p is parallel to OA and the line BC lies in p. Find the equation of p,giving your answer in the form ##ax+by+cz=d##
The Attempt at a Solution
##AB= (4j+k)-(i+2j+3k)=-i+2j-2k, AC= (2i+5j-k)-(i+2j+3k)=i+3j-4k, BC= (2i+5j-k)-(4j+k)=2i+j-2k## i am just groping in the dark here, but i know vectors on same line and parallel vectors should have a scalar or something...relating them