Find the equation of the plane passing throug | vedclass

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(B) The equation of a plane parallel to $ax + by + cz + d = 0$ is given by $ax + by + cz + k = 0$. Since the required plane is parallel to $2x + 3y -

Vedclass · Accepted Answer

$2x + 3y - 4z + 4 = 0$

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(B) The equation of a plane parallel to $ax + by + cz + d = 0$ is given by $ax + by + cz + k = 0$. Since the required plane is parallel to $2x + 3y - 4z = 0$,its equation is of the form $2x + 3y - 4z + k = 0$. This plane passes through the point $(1, 2, 3)$,so we substitute these coordinates into the equation: $2(1) + 3(2) - 4(3) + k = 0$ $2 + 6 - 12 + k = 0$ $8 - 12 + k = 0$ $-4 + k = 0$ $k = 4$. Substituting $k = 4$ back into the equation,we get $2x + 3y - 4z + 4 = 0$.

Find the equation of the plane passing through the point $(1, 2, 3)$ and parallel to the plane $2x + 3y - 4z = 0$.

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