Question 475562: Hello. I need to find an x such that <5,6> and <2,3x> are a)parallel, b)orthogonal, and c)neither. How do i do this?
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website!
<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
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