Discussion
The equation of line joining the points (-3,4,11) and (1,-2,7) is
Answer: B
The line is \(\frac{x+3}{-2} = \frac{y-4}{3} = \frac{z-11}{2}\).
Through \((x_{1}, y_{1}, z_{1}) = (-3, 4, 11)\), the direction is the difference of the two points:
\[ \begin{aligned} (1 - (-3),\ -2 - 4,\ 7 - 11) &= (4, -6, -4) \\ &= -2(-2, 3, 2) \end{aligned} \]
Any multiple of a direction vector is a valid set of direction ratios, so \((-2, 3, 2)\) works, giving the second option. Check: the point \((1, -2, 7)\) gives \(\frac{4}{-2} = \frac{-6}{3} = \frac{-4}{2} = -2\).
Options with \(y + 4\) and \(z + 11\) use the point with the wrong signs. The first option's ratios \((2, 3, 4)\) and the last option's \((-2, -3, -4)\) are not proportional to \((4, -6, -4)\).
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