Discussion
If the line \(\frac{x + 1}{4} = \frac{y + 2}{-3} = \frac{z - \alpha}{-2}\) passes through the point (-1,-2,-3) then the value of \(\alpha\) is
Answer: D
\(\alpha =\) \(-3\).
For \((-1, -2, -3)\) the first two ratios are \(\frac{0}{4} = 0\) and \(\frac{0}{-3} = 0\), so the third must also be zero:
\[ \frac{-3 - \alpha}{-2} = 0 \;\Rightarrow\; \alpha = -3 \]
In fact the point is the line's own base point \((-1, -2, \alpha)\). \(\alpha = 3\) changes the sign, and the other values leave the third ratio non-zero.
A useful habit: when a point's first coordinates already match the line's base point, the parameter is 0, and every remaining coordinate must match too.
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