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Vector along the line of intersection of the planes r.(3i - j + k) = 1 and r.(i + 4j - 2k) = 2

The same question, asked 2 times: 14 May 2024 S2, 21 Apr 2025 S1. Every wording below, oldest first.

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  1. Question 1

    14 May 2024 S2

    118
    A vector parallel to the line of intersection of the planes r⃗⋅(3i^−j^+k^)=1\vec{r}\cdot(3\hat{i}-\hat{j}+\hat{k})=1 and r⃗⋅(i^+4j^−2k^)=2\vec{r}\cdot(\hat{i}+4\hat{j}-2\hat{k})=2 is

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  2. Question 2

    21 Apr 2025 S1

    144
    The line of intersection of the planes r‾⋅(3i^−j^+k^)=1\overline{r}\cdot (3\widehat{i}-\widehat{j}+\widehat{k}) = 1 and  r‾⋅(i^+4j^−2k^)=2\ \overline{r}\cdot (\widehat{i}+ 4\widehat{j}- 2\widehat{k}) = 2 is parallel to the vector

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