Question

(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
Answer this if You know ​

Answer 1

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