Question

Find the equation of the plane passing through the line of intersection of the planes vector r.(i+j+k)=1 and vector r.(2i+3j-k)+4=0 and parallel to x-axis.

Answer 1

Two given planes are

It’* cartesian forms are
x + y + z - 1 = 0 …(i)
and 2x + 3y - z + 4 = 0 …(ii)

Now, equation of plane passing through line of intersection of plane (i) & (ii) is given by

Since (iii) is parallel to x-axis
=> Normal of plane (iii) is perpendicular to x-axis.

[Direction ratios of x-axis are (1, 0, 0)]

Hence, required equation of plane is