A line \( L_{1} \) passing through a point with position vector
P \( \mathbf{p}=\mathbf{i}+2 \mathbf{j}+3 \mathbf{k} \) and parallel \( \mathbf{a}=\mathbf{i}+2 \mathbf{j}+3 \mathbf{k} \), Another line \( L_{2} \)
W passing through a point with position vector \( =2 \mathbf{i}+3 \mathbf{j}+3 \mathbf{k} \) and parallel to \( \mathbf{b}=3 \mathbf{i}+\mathbf{j}+2 \mathbf{k} \).
Equation of plane equidistant from line \( L_{1} \) and \( L_{2} \) is
(a) \( \hat{\mathbf{r}} .(\mathbf{i}-7 \mathbf{j}-5 \mathbf{k})=3 \)
(b) \( \hat{\mathbf{r}} \cdot(\mathbf{i}+7 \mathbf{j}+5 \mathbf{k})=3 \)
(c) \( \hat{\mathbf{r}} .(\mathbf{i}-7 \mathbf{j}-5 \mathbf{k})=9 \)
(d) \( \hat{\mathbf{r}} \cdot(\mathbf{i}+7 \mathbf{j}-5 \mathbf{k})=9 \)
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