If the direction ratios of a line are proportional to 1, -3, 2 then its direction cosines are `1/(sqrt(14)),-3/(sqrt(14)),2/(sqrt(14))` b. `1/(sqrt(14)),2/(sqrt(14)),3/(sqrt(14))` c. `-1/(sqrt(14)),3/(sqrt(14)),2/(sqrt(14))` d. `-1/(sqrt(14)),-2/(sqrt(14)),-3/(sqrt(14))`

Explanation

As the direction ratios of a line are proportional to 1,−3,2.

Then the direction cosines of the line will be

`1/(sqrt(1^2+(-3)^2+2^2)),(-3)/(sqrt(1^2+(-3)^2+2^2)),2/(sqrt(1^2+(-3)^2+2^2))`

`=1/(sqrt14),(-3)/(sqrt14),2/(sqrt14)`

Hence correct option is (a).