Discussion
The equation of a line passing through the point (1,-2,3) and equally inclined to the axes are
Answer: E
The line is \(x - 1 = y + 2 = z - 3\).
A line equally inclined to the three axes has equal direction cosines, so its direction ratios can be taken as \((1, 1, 1)\). Through \((1, -2, 3)\) the line is
\[ \frac{x - 1}{1} = \frac{y + 2}{1} = \frac{z - 3}{1} \]
The other options use the wrong signs for the point: \(y - 2\) would pass through \(y = 2\), and \(z + 3\) through \(z = -3\).
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