What is the equation to the plane through $(1, 2, 3)$ parallel to $3 x + 4 y - 5 z = 0$ ?

3 x + 4 y + 5 z + 4 = 0

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3 x + 4 y - 5 z + 14 = 0

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3 x + 4 y - 5 z + 4 = 0

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3 x + 4 y - 5 z - 4 = 0

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Solution

The correct option is B $3 x + 4 y - 5 z + 4 = 0$
The given equation is $3 x + 4 y - 5 z = 0$
Let the equation of parallel plane be $3 x + 4 y - 5 z = k$ where k is a constant
The plane passes through the point $(1, 2, 3)$
So, $3 \cdot 1 + 4 \cdot 2 - 5 \cdot 3 = k$
$\Rightarrow - 4 = k$
So the equation of the plane is $3 x + 4 y - 5 z = - 4$
$\Rightarrow 3 x + 4 y - 5 z + 4 = 0$
Option C is true

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