Answer :

Given - & . A plane is parallel to both these lines and passes through (1, 2, - 4).


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 direction ratios of the given lines are (2, 3, 6) and (1, 1, - 1)


&






The equation of the plane maybe represented as - 9x + 8y - z + d = 0


Now, this plane passes through the point (1, 2, - 4)


Hence,


(- 9) × 1 + 8 × 2 - (- 4) + d = 0


d = - 11


The Cartesian equation of the plane : - 9x + 8y - z - 11 = 0 i.e. 9x - 8y + z + 11 = 0


The vector equation :


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