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Distance between Two Parallel Planes

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Question

Find the value of $k$ so that the lines $2 x - 3 y = 9$ and $k x - 9 y = 18$ will be parallel.

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Solution

Consider the given equations.

$2 x - 3 y = 9$ ……. (1)

$k x - 9 y = 18$ …….. (2)

Slope of the line (1)

$m_{1} = \frac{2}{3}$

Slope of the line (2)

$m_{2} = \frac{k}{9}$

Since, both lines are parallel.

So, the slopes of both lines are equal.

Therefore,

$m_{1} = m_{2}$

$\frac{2}{3} = \frac{k}{9}$

$k = 6$

Hence, this is the value of $k$ .

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