<5,6> and <2,3x>

To be parallel one must be a multiple of the other:

<5,6> = k<2,3x>

<5,6> = <2k,3kx>



For the first equation k = 

Substitute in the second equation:

6 = 3()x

12 = 3(5x)

12 = 15x

 = x

 = x

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<5,6> and <2,3x>

To be orthogonal their dot product must be 0:

  <5,6>•<2,3x> = 0

(5)(2)+(6)(3x) = 0

        10+18x = 0

           18x = -10

             x = 

             x = 


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To be neither, choose x as anything other than those two values.

Edwin