find the foot of the perpendicular drawn from (-1,3) to line 5x -y-18 = 0
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Answer:
Equation of the line AB
3−4
x−4
=
5−7
y−7
=
3−1
z−1
−1
x−4
=
−2
y−7
=
2
z−1
Consider,
−1
x−4
=
−2
y−7
=
2
z−1
=r
x=−r+4,y=−2r+7,z=2r+1
General point on the line AB is (−r+4,−2r+7,2r+1)
Direction ratios of perpendicular are
−r+4−1,−2r+7−0,2r+1−3
That is
−r+3,−2r+7,2r−2
since perpendicular is on the line AB
Therefore,
−1(−r+3)−2(−2r+7)+2(2r−2)=0
then,
r=
3
7
Therefore,
coordinates of the foot of perpendicular are
(
3
5
,
3
7
,
3
17
)
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