Answer :

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 :


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