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Question
Find the Cartesian equation of the line which passes through the point (−2, 4, −5) and is parallel to the line `(x+3)/3=(4-y)/5=(z+8)/6`
Solution
The equation of the given line is `(x+3)/3=(4-y)/5=(z+8)/6 or (x+3)/3=(y-4)/-5=(z+8)/6`
The required line is parallel to the given line. Therefore, direction ratios of the required line are the same as the direction ratio of the given line. So, the direction ratios of the required line are 3, − 5, 6.
The equation of the straight line passing through (− 2, 4, − 5) and having direction ratios 3, − 5, 6 is
`(x-(-2))/3=(y-4)/-5=(z-(-5))/6`
`(x+2)/3=(y -4)/-5=(z+5)/6`
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