If the line joining points (2, 1, 4) and (a - | vedclass

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(A) The direction ratios of the line joining $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ are $(x_2 - x_1, y_2 - y_1, z_2 - z_1)$.For the first line joinin

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$18, \frac{2}{3}$

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(A) The direction ratios of the line joining $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ are $(x_2 - x_1, y_2 - y_1, z_2 - z_1)$.For the first line joining $(2, 1, 4)$ and $(a - 1, 4, -1)$, the direction ratios are $(a - 1 - 2, 4 - 1, -1 - 4) = (a - 3, 3, -5)$.For the second line joining $(0, 2, b - 1)$ and $(5, 3, -2)$, the direction ratios are $(5 - 0, 3 - 2, -2 - (b - 1)) = (5, 1, -1 - b)$.Since the lines are parallel, their direction ratios must be proportional: $\frac{a - 3}{5} = \frac{3}{1} = \frac{-5}{-1 - b}$.From $\frac{a - 3}{5} = 3$, we get $a - 3 = 15$, so $a = 18$.From $\frac{3}{1} = \frac{-5}{-1 - b}$, we get $3(-1 - b) = -5$, which implies $-3 - 3b = -5$, so $-3b = -2$, and $b = \frac{2}{3}$.Thus, the values of $a$ and $b$ are $18$ and $\frac{2}{3}$ respectively.

If the line joining points $(2, 1, 4)$ and $(a - 1, 4, -1)$ is parallel to the line joining points $(0, 2, b - 1)$ and $(5, 3, -2)$, then the values of $a$ and $b$ are respectively:

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