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Consider the line through points \(A = (1, 1, 2)\) and \(B = (2, 3, 4)\). This line can be parametrized as \((at +b, ct +d, et +f)\)
for some choices of constants \(a, b, c, d, e, \) and \(f\). What is the ordered pair \(\left(\dfrac{c}{a}, \dfrac{e}{a}\right)\)?

 Nov 8, 2019
 #1
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Let the vector  v  be   ( 2 - 1, 3 - 1,4 - 2)  =  ( 1 , 2, 2 )

 

So.....the vector  form of the line  is

 

(1 + t, 1 +2t, 2 + 2t) =    ( t + 1, 2t + 1, 2t + 2)

 

So   c  = 2     e  = 2     a   =  1

 

So    ( c / a , e / a )  =    (   2 / 1 ,   2 / 1)   =    ( 2 , 2) 

 

 

cool cool cool

 Nov 8, 2019

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