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Question
The Cartesian equation of a line AB is: `(2x - 1)/2 = (y + 2)/2 = (z - 3)/3`. Find the direction cosines of a line parallel to line AB.
Solution
We have, `(2x - 1)/2 = (y + 2)/2 = (z - 3)/3`
The equation of line AB can be rewritten as `(x - 1/2)/6 = (y - (-2))/2 = (z - 3)/3`
Thus, direction ratios of the line parallel to AB are proportional to 6, 2, 3.
Hence, the direction cosines of the line parallel to AB are proportional to `6/sqrt(6^2 + 2^2 + 3^2), 2/sqrt(6^2 + 2^2 + 3^2), 3/sqrt(6^2 + 2^2 + 3^2)`
or `6/sqrt(49), 2/sqrt(49), 3/sqrt(49)`
or `6/7, 2/7, 3/7`
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