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Home » If the line drawn from the point (–2, – 1, – 3) meets a plane at right angle at the point (1, – 3, 3), find the equation of the plane.
If the line drawn from the point (–2, – 1, – 3) meets a plane at right angle at the point (1, – 3, 3), find the equation of the plane.
CBSE | Class 12 | Exercise 1 | Maths | NCERT Exemplar | Three Dimensional Geometry
If the line drawn from the point (–2, – 1, – 3) meets a plane at right angle at the point (1, – 3, 3), find the equation of the plane.

According to ques,

Points are :

    \[\left( 2,\text{ }\text{ }1,\text{ }\text{ }3 \right)\text{ }and\text{ }\left( 1,\text{ }\text{ }3,\text{ }3 \right)\]

And,

Direction ratios of the normal to the plane are:

    \[\left( 1\text{ }+\text{ }2,\text{ }-3\text{ }+\text{ }1,\text{ }3\text{ }+\text{ }3 \right)\text{ }=\text{ }\left( 3,\text{ }-2,\text{ }6 \right)\]

Again,

the equation of plane passing through one point (x1, y1, z1) is

    \[a(x\text{ }\text{ }{{x}_{1}})\text{ }+\text{ }b(y\text{ }\text{ }{{y}_{1}})\text{ }+\text{ }c(z\text{ }\text{ }{{z}_{1}})\text{ }=\text{ }0\]

Or,

    \[3\left( x\text{ }\text{ }1 \right)\text{ }\text{ }2\left( y\text{ }+\text{ }3 \right)\text{ }+\text{ }6\left( z\text{ }\text{ }3 \right)\text{ }=\text{ }0\]

Or,

    \[3x\text{ }\text{ }3\text{ }\text{ }2y\text{ }\text{ }6\text{ }+\text{ }6z\text{ }\text{ }18\text{ }=\text{ }0\]

Or,

    \[3x\text{ }\text{ }2y\text{ }+\text{ }6z\text{ }\text{ }27\text{ }=\text{ }0\Rightarrow 3x\text{ }\text{ }2y\text{ }+\text{ }6z\text{ }=\text{ }27\]

hence, the required equation of plane is

    \[3x\text{ }\text{ }2y\text{ }+\text{ }6z\text{ }=\text{ }27.\]

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