Answer :

Given - & . A plane is parallel to both these lines and passes through (3, - 1, 2).


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


& , where the two vectors represent the directions






The equation of the plane maybe represented as 4x + 5y - 17z + d = 0


Now, this plane passes through the point (3, - 1, 2)


Hence,


4 × 3 + 5 × (- 1) – 17 × 2 + d = 0


d = 27


The Cartesian equation of the plane : 4x + 5y - 17z + 27 = 0


The vector equation :


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