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Pair of Lines

Find the equa...

Question

Find the equation of the plane passing through the line of intersection of the planes and and parallel to x-axis.

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Solution

The given planes are

The equation of any plane passing through the line of intersection of these planes is

Its direction ratios are (2λ + 1), (3λ + 1), and (1 − λ).

The required plane is parallel to x-axis. Therefore, its normal is perpendicular to x-axis.

The direction ratios of x-axis are 1, 0, and 0.

Substituting in equation (1), we obtain

Therefore, its Cartesian equation is y − 3z + 6 = 0

This is the equation of the required plane.

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