(a) Parametric form of vector equation (b) Non-parametric form of vector equation (C) Cartesian form of equation of plane

**Equation
of plane containing two non-parallel coplanar lines**

Let be two non-parallel coplanar lines.
Then * *Ã— * *â‰ . Let *P *be any point on the plane
and let _{0} be its position vector. Then, the
vectors * *are also coplanar. So, we get * *. Hence, the vector equation in* *parametric form is .

Let * *be two non-parallel coplanar lines. Then * *Ã— * *â‰ . Let *P *be any point on the plane and let 0 be
its position vector. Then, the vectors * *are
also coplanar. So, we get . Hence, the vector equation in non-parametric form is .

In Cartesian form the equation of the plane containing the two
given coplanar lines

Show that the lines are coplanar. Also,find the non-parametric form of vector equation of the plane containing these lines.

Comparing the two given lines with

We know that the two given lines are coplanar ,

Therefore the two given lines are coplanar.Then we find the non
parametric form of vector equation of the plane containing the two given
coplanar lines. We know that the plane containing the two given coplanar lines
is

which implies that ( - (-*i*Ë† - 3Ë†*j* - 5*k*Ë†)).(7*i*Ë† -14Ë†*j* + 7*k*Ë†) = 0 . Thus, the
required non-parametric vector equation of the plane containing the two given
coplanar lines is . (*i*Ë†* - 2*Ë†*j
+ *Ë†*k* ) = 0.

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

12th Mathematics : UNIT 6 : Applications of Vector Algebra : Equation of plane containing two non-parallel coplanar lines |

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