The direction ratios of a line are (1, -3, 2). Its direction cosines will be:

Question

Question

(1, -3, 2)
(-1, 3, -2)
\(\displaystyle \rm\left({1\over\sqrt{14}},{-3\over\sqrt{14}},{2\over\sqrt{14}}\right)\)
\(\displaystyle\rm\left({-1\over\sqrt{14}},{3\over\sqrt{14}},{-2\over\sqrt{14}}\right)\)

Answer 1

Concept:

If the direction ratios of a line are (l, m, n), then its direction cosines are

\(\rm\displaystyle\left({l\over\sqrt{l^2+m^2+n^2}},{m\over\sqrt{l^2+m^2+n^2}},{n\over\sqrt{l^2+m^2+n^2}}\right)\).

Calculation:

Using the formula for direction cosines from direction ratios, the required direction cosines are:

\(\displaystyle\rm\left({1\over\sqrt{1^2+(-3)^2+2^2}},{-3\over\sqrt{1^2+(-3)^2+2^2}},{2\over\sqrt{1^2+(-3)^2+2^2}}\right)\)

= \(\displaystyle\rm\left({1\over\sqrt{14}},{-3\over\sqrt{14}},{2\over\sqrt{14}}\right)\).