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Question: Answered & Verified by Expert
If $\ell, \mathrm{m}, \mathrm{n}$ and $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are direction cosines of two lines then
MathematicsThree Dimensional GeometryTS EAMCETTS EAMCET 2023 (14 May Shift 1)
Options:
  • A they are parallel when $\ell \mathrm{a}+\mathrm{mb}+\mathrm{nc}=0$
  • B they are perpendicular when $\frac{\ell}{a}=\frac{m}{b}=\frac{n}{c}$
  • C the direction ratios of the bisectors of the angles between the two lines are $\ell \pm \mathrm{a}, \mathrm{m} \pm \mathrm{b}, \mathrm{n} \pm \mathrm{c}$
  • D the direction ratios of the bisectors of the angles between the two lines are $\ell \mathrm{a}, \mathrm{mb}, \mathrm{nc}$
Solution:
1959 Upvotes Verified Answer
The correct answer is: the direction ratios of the bisectors of the angles between the two lines are $\ell \pm \mathrm{a}, \mathrm{m} \pm \mathrm{b}, \mathrm{n} \pm \mathrm{c}$
$\mathrm{L}_1:(l, m, n) ; \mathrm{L}_2:(a, b, c)$
The direction cosine of angle bisector are $l \pm a, m \pm b, n \pm c$

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