Home
Class 12
MATHS
Perpendiculars are drawn from points on ...

Perpendiculars are drawn from points on the line `(x+2)/2=(y+1)/(-1)=z/3` to the plane `x + y + z=3` The feet of perpendiculars lie on the line (a) `x/5=(y-1)/8=(z-2)/(-13)` (b) `x/2=(y-1)/3=(z-2)/(-5)` (c) `x/4=(y-1)/3=(z-2)/(-7)` (d) `x/2=(y-1)/(-7)=(z-2)/5`

A

`(x)/(5)= (y-1)/(8) = (z-2)/(-13)`

B

`(x)/(2)= (y+1)/(3)=(z-2)/(-5)`

C

`(x)/(4)= (y-1)/(3)= (z-2)/(-7)`

D

`(x)/(2)= (y-1)/(-7)= (z-2)/(5)`

Text Solution

Verified by Experts

Any point B on line is `(2lamda-2, -lamda-1, 3lamda)`
Point B lies on the plane for some `lamda`
`rArr" "(2lamda-2)+ (-lamda-1)+ 3lamda=3 or lamda = 3//2`
`rArr" "B-= (1, -5//2, 9//2)`
The foot of the perpendicular from the point `(-2, -1, 0)` on the plane is the point `A(0, 1, 2)`
`rArr" "` Direction ratio of `AB= (1, (-7)/(2), (5)/(2))-= (2, -7, 5)`.
Hence, feet of perpendicular lies on the line
`(x)/(2)= (y-1)/(-7)= (z-2)/(5)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the equation of the projection of the line (x-1)/2=(y+1)/(-1)=(z-3)/4 on the plane x+2y+z=9.

Find the points where line (x-1)/2=(y+2)/(-1)=z/1 intersects x y ,y z and z x planes.

Equation of a line in the plane pi =2x-y+z-4=0 which is perpendicular to the line l whose equation is (x-2)/1=(y-2)/(-1)=(z-3)/(-2) and which passes through the point of intersection of l and pi is (A) (x-2)/1=(y-1)/5=(z-1)/(-1) (B) (x-1)/3=(y-3)/5=(z-5)/(-1) (C) (x+2)/2=(y+1)/(-1)=(z+1)/1 (D) (x-2)/2=(y-1)/(-1)=(z-1)/1

Find the value of 'p' if the lines (x-5)/7=(y+2)/(-5)=z/1 and x/1=y/p=z/3 are perpendicular .

The straight lines (x-3)/(2)=(y+5)/(4)=(z-1)/(-13)and(x+1)/(3)=(y-4)/(5)=(z+2)/(2) are

Find the point of intersection of the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-4)/(5)=(y-1)/(2)=z .

The line through of the plane passing through the lines (x-4)/(1)=(y-3)/(1)=(z-2)/(2) and (x-3)/(1)=(y-2)/(-4)=(z)/(5) is

Find the value of p so that the lines (x-5)/7=(y+2)/(-5)=z/1 and x/p=y/2=z/3 are perpendicular to each other.

Show that the lines (x-1)/(3)=(y+1)/(2)=(z-1)/(5)and(x+2)/(4)=(y-1)/(3)=(z+1)/(-2) do not intersect.