If the direction cosines of two lines are 23, 23, 13 and 513, 1213, 0, then identify the direction ratios of a line which is bisecting one of the angle between them.

AP EAMCET · Maths · Three Dimensional Geometry

If the direction cosines of two lines are $(\frac{2}{3}, \frac{2}{3}, \frac{1}{3})$ and $(\frac{5}{13}, \frac{12}{13}, 0)$ , then identify the direction ratios of a line which is bisecting one of the angle between them.

A $⟨ 40, 60, 13 ⟩$
B $⟨ 41, 60, 10 ⟩$
C $⟨ 41, 62, 13 ⟩$
D $⟨ 1, 2, 3 ⟩$

Verified Solution

Answer & Solution

Correct Answer

(C) $⟨ 41, 62, 13 ⟩$

Step-by-step Solution

Detailed explanation

Given, the direction cosines of two lines are 23, 23, 13 and 513, 1213, 0. We know that, the direction ratios of the line bisecting the angle between the lines whose direction cosines are l1, m1, n1 and l2, m2, n2 are proportional to…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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