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# Calculus - Vectors - Area of Triangle, Volume of Parallepipe

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Question (1)
a = (3 , 1 , 2 ) , b = ( - 1 , 1 , 0 ) , c = ( 0 , 0 , - 4 ) , then show that a × ( b × c ) &#8800; (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

https://brainmass.com/math/calculus-and-analysis/calculus-vectors-area-triangle-volume-parallepipe-113177

#### Solution Preview

Given a = (3 , 1 , 2 ) , b = ( - 1 , 1 , 0 ) , c = ( 0 , 0 , - 4 )
a × ( b × c ) = 8 i - 8 j - 8 k and (a × b) × c = 8 i - ...

#### Solution Summary

The solution to the posted problems in Calculus on Vector Product, Finding Area of Triangle, Finding Orthogonal Vector to a Plane, Finding Area of Parallelopiped using vectors are given with step by step explanation with all the procedure and working so that student could use these solutions as model solutions to solve other similar problems

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