(35) The foot of the perpendicular from (1, 2) on the line x - 3y + 7 = 0 is
(a) (5/4, 5/13) (b) (4/5, 13/5) (c) (4/5, 9/5) (d) none of these
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Answer:
Let L be the foot of perpendicular drawn from the point to the given line.
And the given line is
5
x+3
=
2
y−1
=
3
z+4
=t Consider
Therefore, x=5t−3,y=2t+1,z=3t−4
which is direction ratios of this line
and also the point (0,2,3)
0(5t−3)+2(2t+1)+3(3t−4)=0
Since they are perpendicular.
4t+2+9t−12=0
t=
13
10
So, coordinates of L are x=5(
13
10
)−3,y=2(
13
10
)+1,z=3(
13
10
)−4;x=
13
11
,y=
13
33
,z=
13
−22
Foot of perpendicular from the point (0,2,3) is (
13
11
,
13
33
,
13
−22
)
And the length
=
(
13
11
−0)
2
+(
13
33
−2)
2
+(
13
−22
−3)
2
=
(
13
11
)
2
+(
13
7
)
2
+(
13
−61
)
2
=4.8 sq. units
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