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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.**

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, (* *âˆ’ )
lies in the plane containing * *and .

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

, where s, t âˆˆ **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 .

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 .

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

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

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 |

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