TS EAMCET · Maths · Three Dimensional Geometry
If \(\ell, \mathrm{m}, \mathrm{n}\) and \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are direction cosines of two lines then
- 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 \(\ell \mathrm{a}, \mathrm{mb}, \mathrm{nc}\)
Answer & Solution
Correct Answer
(C) the direction ratios of the bisectors of the angles between the two lines are \(\ell \pm \mathrm{a}, \mathrm{m} \pm \mathrm{b}, \mathrm{n} \pm \mathrm{c}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{L}_1:(l, m, n) ; \mathrm{L}_2:(a, b, c)\) The direction cosine of angle bisector are \(l \pm a, m \pm b, n \pm c\)
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