Discussion
The equation of line which is parallel to \(\frac{2 - x}{-3} = \frac{y - 2}{2} = \frac{z - 4}{1}\) and passing through the point (1,1,1) , is
Answer: B
The line is \(\frac{x - 1}{3} = \frac{y - 1}{2} = \frac{z - 1}{1}\).
First put the given line in standard form. \(\frac{2 - x}{-3} = \frac{x - 2}{3}\), so the line is \(\frac{x - 2}{3} = \frac{y - 2}{2} = \frac{z - 4}{1}\), with direction ratios 3, 2, 1.
A parallel line through (1, 1, 1) has the same direction ratios, giving the keyed equation. Taking the -3 at face value gives direction (-3, 2, 1), which ignores the sign of \(2 - x\). The options with \(z + 1\) pass through \(z = -1\), not 1.
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