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Intercept Form of a Line

Find the equa...

Question

Find the equation of the plane which contains the line of intersection of the planes , and which is perpendicular to the plane .

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Solution

The equations of the given planes are

The equation of the plane passing through the line intersection of the plane given in equation (1) and equation (2) is

The plane in equation (3) is perpendicular to the plane,

Substituting in equation (3), we obtain

This is the vector equation of the required plane.

The Cartesian equation of this plane can be obtained by substituting in equation (3).

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Q. The equation of the plane passing through the line of intersection of the planes

\to r \cdot (2^i - 3^j + 4^k) = 1

\to r \cdot (^i -^j) + 4 = 0

and perpendicular to the plane

\to r \cdot (2^i -^j -^k) + 4 = 0,

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

Q. A unit vector parallel to the intersection of the planes

\to r \cdot (^i -^j +^k) = 5

\to r \cdot (2^i +^j - 3^k) = 4

Q. The distance between the line

\to r = 2^i - 2^j + 3^k + λ (^i -^j + 4^k)

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Q. Prove that equation of the plane passing through (1, 2, 3) and perpendicular to planes

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\to r . (^i - 2^j -^k) = 0

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