The two lines L1 : r→=(i^+5j^+5k^)+t(4i^-4j^+5k^) and L2 : r→=(2i^+4j^+5k^)+s(8i^-3j^+k^) are such that

(D) both are non-Skew lines, non-parallel, non-perpendicular

TS EAMCET · Maths · Three Dimensional Geometry

The two lines $L_{1} : \vec{r} = (\hat{i} + 5 \hat{j} + 5 \hat{k}) + t (4 \hat{i} - 4 \hat{j} + 5 \hat{k})$ and $L_{2} : \vec{r} = (2 \hat{i} + 4 \hat{j} + 5 \hat{k}) + s (8 \hat{i} - 3 \hat{j} + \hat{k})$ are such that

A both are parallel
B both are perpendicular
C both are Skew lines
D both are non-Skew lines, non-parallel, non-perpendicular

Verified Solution

Answer & Solution

Correct Answer

(C) both are Skew lines

Step-by-step Solution

Detailed explanation

Two lines r→=a→1+λb→1 and r→=a→2+λb→2 are parallel if b→1=mb→2, for m∈R and perpendicular if b→1·b→2=0 and intersects, if distance between them =0. We have lines…

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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