Q. 1

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

Answer :

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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