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