Home
Class 12
MATHS
The equation of the plane through the li...

The equation of the plane through the line of intersection of the planes `ax + by+cz + d= 0` and `a'x + b'y+c'z + d'= 0` parallel to the line `y=0` and `z=0` is

A

`(ab'-a'b)x+(bc'-b'c)y+(ad'-a'd)=0`

B

`(ab'-a'b)x+(bc'-b'c)y+(ad'-a'd)z=0`

C

`(ab'-a'b)y+(bc'-b'c)z+(ad'-a'd)=0`

D

none of these

Text Solution

Verified by Experts

The equation of a plane through the line of intersection of the planes `ax+by+cz+d=0` and
`" "a'x+b'y+c'z+d'=0` is
`" "(ax+by+cz+d)+lamda(a'x+b'y+c'z+d')=0` ltBrgt or `" "x(a+lamdaa')+y(b+lamdab')+z(c+lamdac')+ d+ lamdad'=0`
This is parallel to the x-axis, i.e., y = 0, z = 0.
Therefore,
`" "1(a+lamdaa')+ 0(b+lamdab')+ 0(c+ lamdac')=0`
or `" "lamda= (c)/(a')`
Putting the value of the `lamda` in (i) , the required plane is
`" "y(a'b-ab')+ z(a'c-ac')+ a'd-ad'=0`
or `" "(ab'-a'b)y + (ac'-a'c)z+ ad' -a'd=0`
Promotional Banner

Similar Questions

Explore conceptually related problems

The equation of the plane through the line of intersection of planes ax + by + cz + d=0 , a 'x + b'y + c'z + d' =0 and parallel to the lines y =0 and z=0 is

The equation of the plane passing through the line of intersection of the planes ax + by+cz + d = 0 and lx + my + nz + p = 0 and it is parallel to the line y = 0 z = 0 is..............

The equation of the plane passing through the line of intersection of the planes x+y+z+3 =0 and 2x-y + 3z +2 =0 and parallel to the line (x)/(1) = (y)/(2) = (z)/(3) is

Find the equation of the plane through the line of intersection of the planes: x+3y-z+1=0 and x+y-2z+3=0 and perpendicular to the plane 3x-y-2z-4=0

Find the equation of the plane through the line of intersection of the planes x+2y+3z+4=0\ a n d\ x-y+z+3=0 and passing through the origin.