(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find a vector equation of the line l containing the points (1,3,1) and (1,-3,-1). Find the perpendicular distance of the point with coordinates (2,-1,1) from l.

2. The attempt at a solution

Let (1,3,1) =a, let (2,-1,1) =q. Let N be the point where ANQ = 90 degrees.

r= (1,3,1) + t(1-1,-3-3,-1-1) = (1,3,1) + t(0,-6,-2)

|p| = sqrt (6^2 + 2^2) = 2 sqrt 10

Unit vector,u= (-3 sqrt 10/10)i+ (- sqrt 10/10)j

Vector AQ =q-a=i- 4j

AN = (Vector AQ).u= 6 sqrt 10/5

Hence, perpendicular distance NQ = sqrt (|Vector AQ|^2 - AN^2) = 17 - (6 sqrt 10/5)^2 = sqrt 65/5.

3. Relevant equations

The book gives the answer AN = 21 sqrt 15/5. Can anyone please check my answer for any mistakes? Thanks.

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# Homework Help: Finding perpendicular distance of a point from line l (using vector equation).

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