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Question
Find the direction ratio and direction cosines of a line parallel to the line whose equations are 6x − 12 = 3y + 9 = 2z − 2
Solution
The equations of the line are 6x − 12 = 3y + 9 = 2z − 2, which, when written in standard symmetric form, will be `(x - 2)/(1/6) = (y-(-3))/(1/3) = (z - 1)/(1/2)`
Since, lines are parallel, we have `a_1/a_2 = b_1/b_2 = c_1/c_2`
Hence, the required direction ratios are `(1/6, 1/3, 1/2)` or (1, 2, 3) and the required direction cosines are `(1/sqrt(14), 2/sqrt(14), 3/sqrt(14))`
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