Let L1 (respectively L2 ) be the line passing through 2i^-k^ (respectively 2i^+j^-3k^) and parallel to 3i^-j^+2k^ (respectively i^-2j^+k^). Then the shortest distance between the lines L1 and L2 is equal to

AP EAMCET · Maths · Three Dimensional Geometry

Let $L_{1}$ (respectively $L_{2}$ ) be the line passing through $2 \hat{i} - \hat{k}$ (respectively $2 \hat{i} + \hat{j} - 3 \hat{k}$ ) and parallel to $3 \hat{i} - \hat{j} + 2 \hat{k}$ (respectively $\hat{i} - 2 \hat{j} + \hat{k}$ ). Then the shortest distance between the lines $L_{1}$ and $L_{2}$ is equal to

A $\frac{10}{\sqrt{35}}$
B $\frac{8}{\sqrt{35}}$
C $\frac{11}{\sqrt{35}}$
D $\frac{9}{\sqrt{35}}$

Verified Solution

Answer & Solution

Correct Answer

(D) $\frac{9}{\sqrt{35}}$

Step-by-step Solution

Detailed explanation

Given that line L1 passes through 2i^-k^ and parallel to 3i^-j^+2k^ and line L2 passes through 2i^+j^-3k^ and parallel to i^-2j^+k^. Then, a1=2i^-k^, b1=3i^-j^+2k^ and a2=2i^+j^-3k^, b2=i^-2j^+k^ Shortest distance between lines is given by,…

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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