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Question
Find the Cartesian equation of the line which passes through the point (−2, 4, −5) and parallel to the line given by `(x+3)/3 = (y-4)/5 = (z+8)/6`.
Solution
The required line is parallel to the line `(x + 3)/3 = (y - 4)/5 = (z + 8)/6`.
∴ The direction ratios of the required line are 3, 5, and 6, and they pass through the points (−2, 4, −5).
∴ Equation of the required line
`(x - (-2))/3 = (y - 4)/5 = (z - (-5))/6`
or `(x + 2)/3 = (y - 4)/5 = (z + 5)/6`
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