alleryA line passes through the points $(1, 2, 3)$ and $(4, 6, 9)$. The direction ratios of the line are:
- $(4, 6, 9)$
- $(3, 4, 6)$
- $(5, 8, 12)$
- $(1, 2, 3)$
Show answer and solution
Correct answer: B. $(3, 4, 6)$
Direction ratios of the line joining two points are the differences in coordinates: $(x_2 - x_1, y_2 - y_1, z_2 - z_1)$.
Here: $(4 - 1, 6 - 2, 9 - 3) = (3, 4, 6)$.
Direction ratios are not unique. $(6, 8, 12)$ or $(1.5, 2, 3)$ would also be valid since multiplying by any non-zero scalar preserves the direction. The standard answer just uses the raw differences.
Direction cosines (the normalised version) are $(3, 4, 6) / \sqrt{9 + 16 + 36} = (3, 4, 6) / \sqrt{61}$.