Finding the Nonzero Vector and Area of Triangle

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Homework Statement



Find a nonzero vector orthogonal to the plane through the point P, Q,and R. (b) also find the area of triangle PQR

P(1,0,1) , Q(-2,1,3) , R(4,2,5)

Homework Equations


-Cross product
-Finding the Angle
-Area formula

The Attempt at a Solution



My steps:
1. i found the vectors for PQ = <-3,1,2> and PR = <3,2,4>

2. i perform the cross product (PQ X PR), which got me <0,18,-9>

Can anyone help me?
 
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NVM, i just solved it!
 
It is a basic property of the cross product that the length of the cross product of vectors u and v is the area of the parallelogram having vectors u and v as to adjacent sides and so 1/2 the length of their cross product is the area of the triangle having u and v as sides.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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