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Straight lines in 3D

Question

The perpendicular distance of the point (2,4,-1) from line x+51=y+34=z69 is

Moderate
Solution

A=(2,4,1),

Any point on the line P=(t5,4t3,9t+6)
Let P be the foot of the perpendicular of A
AP  is perpendicular to given line.
Use formula a1a2+b1b2+c1c2=0 , t = 1

point P(-4,1,-3)

find distance between PandA



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