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Find the distance between Q = (3, -7, -1) and the line through A = (1, 1, 2) and B = (2, 3, 4) This distance is equal to \(\dfrac{\sqrt{d}}{3}\)
for some integer d. What is d?

 Mar 16, 2019
 #1
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\(\hat{u} = B-A\\ d = \dfrac{\|AQ \times \hat{u}\|}{\|\hat{u}\|}\)

 

\(\hat{u} = (1,2,2)\\ \|\hat{u}\|=3\\ AQ = Q-A=(2,-8,-3)\\ \dfrac{\|AQ \times \hat{u} \|}{\|u\|}= \dfrac{\|(-10, -7, 12)\|}{3} = \dfrac{\sqrt{293}}{3}\\ d=293\)

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 Mar 16, 2019

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