Find the vector equation of the plane passing through the point and parallel to the vectors and

Given - & are two lines to which a plane is parallel and it passes through the point

To find – The equation of the plane

Tip – A plane parallel to two vectors will have its normal in a direction perpendicular to both the vectors, which can be evaluated by taking their cross product

The equation of the plane maybe represented as 5x + 2y - 3z + d = 0

Now, this plane passes through the point (3, 4, 2)

Hence,

5 × 3 + 2 × 4 – 3 × 2 + d = 0

⇒ d = - 17

The Cartesian equation of the plane : 5x + 2y - 3z - 17 = 0 i.e. 5x + 2y - 3z = 17

The vector equation :