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Decide whether two lines are parallel, intersecting or skew

This type of question, asked 3 times: 25 Apr 2025 S2, 26 Apr 2025 S2, 16 Apr 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    25 Apr 2025 S2

    131
    The lines rˉ=(i^+j^−k^)+λ(3i^−j^)\bar{r}= (\widehat{i}+\widehat{j}-\widehat{k}) +\lambda(3\widehat{i}-\widehat{j}) and r‾=(4i^−k^)+μ(2i^+3k^)\overline{r}= (4\widehat{i}-\widehat{k}) +\mu(2\widehat{i}+ 3\widehat{k}) are

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  2. Question 2

    26 Apr 2025 S2

    131
    The lines 6x−618=y+13=z−15\frac{6x- 6}{18}=\frac{y+ 1}{3}=\frac{z- 1}{5} and 3x+612=y−13=z+12\frac{3x+ 6}{12}=\frac{y- 1}{3}=\frac{z+ 1}{2} are...

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  3. Question 3

    16 Apr 2026 S1

    92
    The lines x−1−1=y+21=z−3−2\dfrac{x - 1}{-1} = \dfrac{y + 2}{1} = \dfrac{z - 3}{-2} and x−11=y+21=z+1−2\dfrac{x - 1}{1} = \dfrac{y + 2}{1} = \dfrac{z + 1}{-2} are

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