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Question
Find the Cartesian equations of the line which passes through the point (–2, 4, –5) and parallel to the line `(x + 2)/(3) = (y - 3)/(5) = (z + 5)/(6)`.
Solution
The line `(x + 2)/(3) = (y - 3)/(5) = (z + 5)/(6)` has direction ratios 3, 5, 6.
The required line has direction ratios 3, 5, 6 as it is parallel to the given line.
It passes through the point (– 2, 4, – 5).
The cartesian equation of the line passing through (x1, y1, z1) and having direction ratios a, b, c are
`(x- x_1)/a = (y- y_1)/b = (z - z_1)/c`
∴ The required cartesian equation of the line are
`(x - (-2))/(3) = (y - 4)/(5) = (z - (-5))/(6)`
i.e. `(x + 2)/(3) = (y - 4)/(5) = (z + 5)/(6)`.
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