Calculus - Vectors - Area of Triangle, Volume of Parallepipe

Question (1)
a = (3 , 1 , 2 ) , b = ( - 1 , 1 , 0 ) , c = ( 0 , 0 , - 4 ) , then show that a × ( b × c ) ≠ (a × b) × c

Question(2)
Given P ( 2 , 1 , 5 ), Q = ( - 1 , 3 , 4 ) and R = ( 3 , 0 , 6 ), then find (a) a vector orthogonal to the plane through the points P,Q and R (b) Find the area of the triangle PQR.

Question(3)
Given, P = ( 0 , 1 , 2 ) , Q = ( 2 , 4 , 5 ), R = ( - 1 , 0 , 1 ) and S = ( 6 , - 1 , 4 )
Find the Volume of the Parallelopiped with adjacent edges PQ, PR and PS.

The full detailed step by step solution is given in the attached solution file vectors.doc

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