Home
Class 12
MATHS
If the distance between the plane Ax 2y...

If the distance between the plane Ax 2y + z = d and the plane containing the lines 2 1x = 3 2y = 4 3z and 3 2x = 4 3y = 5 4z is 6 , then |d| is

Text Solution

Verified by Experts

The correct Answer is:
`|d|=6`
Equation of the plane containing the lines
`(x-2)/(2)=(y-3)/(5)" and "(x-1)/(2)=(y-2)/(3)=(z-3)/(4)`
is `a(x-2)+b(gamma-3)+c(z-4)=0" "...(i)`
where, `3a+4b+5c=0" "…(ii)`
`2a+3b+4c=0" "(iii)`
and`a(1-2)+b(2-3)+c(2-3)=0`
i.e.`" "a+b+c=0" "...(iv)`
From Eqs. (ii) and (iii), `(a)/(1)=(b)/(-2)=(c)/(1),` which satisfy Eq. (iv).
Plane through lines is `x-2y+z=0.`
Given plane is `Ax-2y+z=d` is `sqrt(6).`
`:.` Planes must be parallel, so A=1 and then
`(|d |)/(sqrt(6))=sqrt(6)implies|d|=6`
Promotional Banner

Similar Questions

Explore conceptually related problems

If the distance between the plane Ax-2y+z=d and the plane containing the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-2)/(3)=(y-3)/(4)=(z-4)/(5) is sqrt(6) , then |d| is equal to….

If the distance between the plane Ax-2y+z=d .and the plane containing the lies (x+1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-2)/(3)=(4-3)/(4)=(z-4)/(5) is sqrt(6), then |d| is

Find the distance between the planes 2x-y+2z=4 and 6x-3y+6z=2.

Find the distance between the planes 2x+3y+4z=4 and 4+6y+8z=12 .

Find the distance between the planes x+2y+3z+7=0 and 2x+4y+6z+7=0 .

The angle between the line x/2 = y/3 = z/4 and the plane 3 x + 2y -3z =4 is