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Chapter: 12th Mathematics : UNIT 6 : Applications of Vector Algebra

Equation of a plane passing through a given point and parallel to two given non-parallel vectors

Equation of a plane passing through a given point and parallel to two given non-parallel vectors

Equation of a plane passing through a given point and parallel to two given non-parallel vectors.


(a) Parametric form of vector equation

Consider a plane passing through a given point A with position vector  and parallel to two given non-parallel vectors  and . If  is the position vector of an arbitrary point P on the plane, then the vectors  and  are coplanar. So, ( − ) lies in the plane containing  and .

Then, there exists scalars s, t R  such that  which implies

 , where s, t R ... (1)

This is the parametric form of vector equation of the plane passing through a given point and parallel to two given non-parallel vectors .


(b) Non-parametric form of vector equation

Equation (1) can be equivalently written as


which is the non-parametric form of vector equation of the plane passing through a given point and parallel to two given non-parallel vectors .


(c) Cartesian form of equation


This is the Cartesian equation of the plane passing through a given point and parallel to two given non-parallel vectors.

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12th Mathematics : UNIT 6 : Applications of Vector Algebra


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