Answer :
Distance between point and line = [tex]\frac{\sqrt{261} }{3}[/tex]
Distance
- The distance between two points is the length of the line joining the two points.
- If the two points lie on the same horizontal or same vertical line, the distance can be found by subtracting the coordinates that are not the same.
Given that,
Given point (6, -4 , 1)
Given equation of line
x = 2t, y = t − 3, z = 2t + 2
The directional vector of the given line is
<2 , 1 , 2> at t =0 the point <0, -3 , 2> is on the line.
Distance between point and line
= | < 0-6, -3 + 4 , 2-1 > x <2 , 1, 2>| / [tex]\sqrt{2^{2} + 1^{2} + 2^{2}[/tex]
= |<-6 , 1 , 1> x <2 , 1 , 2 >| / [tex]\sqrt{9}[/tex]
<-6 , 1 , 1 > x < 2, 1, 2 > = (2 - 1)i - (-12 -2) j + (-6 -2) k
= i + 14 j - 8k
|<-6 , 1 , 1> x < 2, 1, 2>| = [tex]\sqrt{1^{2} + 14^{2} + -8^{2} }[/tex]
= [tex]\sqrt{261}[/tex]
Hence , distance between the point and line = [tex]\frac{\sqrt{261} }{3}[/tex]
To learn more about Distance check the given link
https://brainly.com/question/29722875
#SPJ4
