- #1
Alshia
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Homework Statement
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.