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Question
Find the Cartesian equations of the line passing through A(2, 2, 1) and B(1, 3, 0).
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Solution
The cartesian equations of the line passing through the points (x1, y1, z1) and (x2, y2, z2) are
`(x - x_1)/(x_2 - x_1) = (y - y_1)/(y_2 - y_1) = (z - z_1)/(z_2 - z_1)`
Here, (x1, y1, z1) ≡ (2, 2, 1) and (x2, y2, z2) ≡ (1, 3, 0)
∴ The required cartesian equations are
`(x - 2)/(1 - 2) = (y - 2)/(3 - 2) = (z - 1)/(0 - 1)`
i.e. `(x - 2)/(-1) = (y - 2)/(1) = (z - 1)/(-1)`.
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