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Distance Formula

If the lines ...

Question

If the lines $\frac{x - 0}{1} = \frac{y + 1}{2} = \frac{z - 1}{- 1}$ and $\frac{x + 1}{k} = \frac{y - 3}{- 2} = \frac{z - 2}{1}$ are at right angles, then the value of k is

A

5

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B

0

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C

3

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D

- 1

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Solution

The correct option is A $5$
If $(l_{1} m_{1} n_{1})$ and $(l_{2} m_{2} n_{2})$ are directions of two $⊥$ lines then,
$l_{1} l_{2} + m_{1} m_{2} + n_{1} n_{2} = 0 k - 4 - 1 = 0 k = 5$

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