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(A) The equation of a plane parallel to $ax + by + cz + d = 0$ is given by $ax + by + cz + k = 0$.Given the plane $x + 2y + 5z = 0$,any plane parallel

Vedclass · Accepted Answer

$(x - 1) + 2(y - 2) + 5(z - 3) = 0$

Vedclass · Answer

(A) The equation of a plane parallel to $ax + by + cz + d = 0$ is given by $ax + by + cz + k = 0$.Given the plane $x + 2y + 5z = 0$,any plane parallel to it will have the form $x + 2y + 5z + k = 0$.Since this plane passes through the point $(1, 2, 3)$,we substitute these coordinates into the equation:$(1) + 2(2) + 5(3) + k = 0$$1 + 4 + 15 + k = 0$$20 + k = 0$$k = -20$Substituting $k = -20$ back into the equation,we get $x + 2y + 5z - 20 = 0$,or $x + 2y + 5z = 20$.Comparing this with the given options,the equation $(x - 1) + 2(y - 2) + 5(z - 3) = 0$ simplifies to $x - 1 + 2y - 4 + 5z - 15 = 0$,which is $x + 2y + 5z - 20 = 0$. Thus,option $A$ is correct.

The equation of the plane passing through the point $(1, 2, 3)$ and parallel to the plane $x + 2y + 5z = 0$ is

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