Discussion
If the point (3,6, k) lie on the line \(\frac{x-1}{1} = \frac{y-2}{2} = \frac{z-3}{3}\), then the value of k is
Answer: C
k is 9.
Put x = 3 and y = 6 into the equation of the line:
\[ \frac{3 - 1}{1} = \frac{6 - 2}{2} = 2 = \frac{k - 3}{3} \]
The first two fractions agree, so the point can lie on the line, and \(k - 3 = 6\) gives k = 9. 2 is the common value of the fractions, not k, and 3 is the z-coordinate of the base point (1, 2, 3).
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