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Find the value of \(x \) such that \(\mathbf{v} = \begin{pmatrix} 1 \\ 2 \\ x \end{pmatrix}\)is a vector parallel to the plane through the points \(A = (0,1,1), B = (1,1,0)\) and \(C = (1,0,3).\)

 Nov 8, 2019
 #1
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Here : https://web2.0calc.com/questions/please-help_34243

 

We found that the normal vector to the plane containing A, B , C  was

 

(-1, - 3 , - 1)

 

The dot product  of  any vector  parallel  to the plane and the normal vector to the plane will  =  0

 

So  using  ( 1, 2 , x)     we have that

 

1(-1) + 2(-3)  + x (-1)  =  0

 

-1  - 6  -  x  =  0

 

-7  - x  =  0

 

-7  = x

 

cool cool cool

 Nov 8, 2019

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