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Equation of a Plane : Vector Form

Equation of a...

Question

Equation of a plane passing through the intersection of the planes $x + y - z + 2 = 0$ and $x - y + z + 3 = 0$ and which intersects exactly one coordinate axis, is?

A

2 x - 5 = 0

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B

2 x + 5 = 0

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C

3 y + 5 = 0

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D

3 y - 5 = 0

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Solution

The correct option is A $2 x + 5 = 0$
Equation of plane passing through the antersection of the planes will be
$x + y - z + p (x - y + 2 + 3) = 0$ ..(i)
This plane will be $⊥$ to line having direction ratio's (0, 1, 1) and product of this will give $a = 1$ which gives equation of plane.
$2 x + 5 = 0$

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Similar questions

Q. Equation of the plane passing through the intersection of the planes

x + y + z = 6

2 x + 3 y + 4 z + 5 = 0

(1, 1, 1)

Q. Find the equation of the plane which passes through the line of intersection of the planes

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x - 5 y + z + 6 = 0

and is parallel to the line

x + y - z + 8 = 0 = x - y - z + 2

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x + y + z - 4 = 0

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and whose x intercept equal to unity

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

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which is perpendicular to the plane

x - y + z = 0

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and parallel to the line

\frac{x - 1}{2} = \frac{y - 3}{4} = \frac{z - 5}{5}

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