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

Options

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

Answer

c

Explanation

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`