Q. 295.0( 1 Vote )

Find the equation

Answer :

Given: equation of the planes and

To find: the equation of the plane passing through the line of intersection of the two givenand parallel to the x-axis.

The given equation of planes can be written in the Cartesian form, as shown below



Hence given equation of planes can be written in Cartesian form are



The equation of a plane passing through the line of intersection of these two planes is,


x+y+z-1+2 λx+3 λy-z λ+4λ=0


Now, direction ratios of normal to the plane (iii), are,

a1=1+2λ, b1=1+3λ, c1=1-λ

Now the direction ratios of x-axis are,

a2=1, b2=0, c2=0

Since the required plane (iii) is parallel to x-axis, then

a1a2+b1b2+ c1c2=0

Substituting the corresponding values, we get




So substituting the value of λ in equation (iii), we get



Is the required equation of the plane, it can also be written as

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