Assignment:
Q1) a. Find the (vector) equation of the plane passing through the points (1,2,-2), (-1,1,-9), (2,-2,-12).
b. Find the (vector) equation of the plane containing (1,2,-1) and perpendicular to (3,-1,2).
Q2) Suppose a, b, c are non zero vectors.
a. Explain why (a x b) x (a x c) is in the direction of a.
b. Show that (a x b) x (a x c ) = ( a . b x c) a.
c. Show that a x b . (b x c) x (c x a) = (a . b x c)²
Provide complete and step by step solution for the question and show calculations and use formulas.