If $L_{1}$ is a line through the point $5 i + 8 j + 11 k$ and parallel to the vector $2 i + 3 j + 4 k$ and $L_{2}$ is a line through the point $4 i + 6 j + 8 k$ and parallel to the vector $3 i + 4 j + 5 k$ , then the point of intersection of $L_{1}$ and $L_{2}$ is

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$i + 2 j + 3 k$

$i - 2 j + 2 k$

$2 i + 3 j + k$

$i + j + k$

answer is B.

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Detailed Solution

$L_{1} \Rightarrow r = (5 i + 8 j + 11 k) + t (2 i + 3 j + 4 k) L_{2} \Rightarrow r = (4 i + 6 j + 8 k) + μ (3 i + 4 j + 5 k) compare coff i, j coff \begin{matrix} 5 + 2 t = 4 + 3 μ \\ 2 t = - 1 + 3 μ \end{matrix} \begin{matrix} 8 + 3 t = 6 + 4 μ \\ 3 (\frac{3 μ + 1}{2}) = - 2 + 4 μ \\ 9 μ - 3 = - 4 + 8 μ \\ μ = - 1 \end{matrix} r = i + 2 j + 3 k$