Discussion
A straight line through the point (1,-1,0) meets the line \(\frac{x - 1}{1} = \frac{y + 1}{1} = \frac{z - 1}{-1}\) at right angle . It's equation is
Answer: A
The line is \(\frac{x - 1}{1} = \frac{y + 1}{1} = \frac{z}{2}\).
A general point of the given line is \((1 + t, -1 + t, 1 - t)\). The direction from (1, −1, 0) to it is \((t, t, 1 - t)\), and this must be perpendicular to the line's direction (1, 1, −1):
\[ t + t - (1 - t) = 0 \Rightarrow t = \frac{1}{3} \]
The direction is then \(\left(\frac{1}{3}, \frac{1}{3}, \frac{2}{3}\right) \propto (1, 1, 2)\), giving option A. Option E has direction (1, 1, −2), which is not perpendicular to (1, 1, −1), and options B, C and D do not pass through (1, −1, 0).
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