Q1 of 181 Page 1237

Find the vector and Cartesian equations of the plane passing through the origin and parallel to the vectors and

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


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 plane passes through origin (0, 0, 0).


Formula to be used – If a line passes through the point (a, b, c) and has the direction ratios as (a’, b’, c’), then its vector equation is given by where λ is any scalar constant


The required plane will be




The vector equation :


The Cartesian equation : x + 2y + 3z = 0


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