The equation of a plane parallel to the x-axi | vedclass

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(C) The general equation of a plane is given by $ax + by + cz + d = 0$,where $(a, b, c)$ are the direction ratios of the normal to the plane.If a plan

Vedclass · Accepted Answer

$by + cz + d = 0$

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(C) The general equation of a plane is given by $ax + by + cz + d = 0$,where $(a, b, c)$ are the direction ratios of the normal to the plane.If a plane is parallel to the $x$-axis,its normal must be perpendicular to the $x$-axis.The direction ratios of the $x$-axis are $(1, 0, 0)$.Since the normal $(a, b, c)$ is perpendicular to the $x$-axis $(1, 0, 0)$,their dot product must be zero:$a(1) + b(0) + c(0) = 0 \implies a = 0$.Substituting $a = 0$ into the general equation,we get $0x + by + cz + d = 0$,which simplifies to $by + cz + d = 0$.Therefore,the correct option is $C$.

The equation of a plane parallel to the $x$-axis is:

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