The value of \( \lambda \) for which the angle between lines
\( \vec{r} = \hat{i} + \hat{j} + \hat{k} + p(2\hat{i} + \hat{j} + 2\hat{k}) \)
and
\( \vec{r} = (1+q)\hat{i} + (1+q\lambda)\hat{j} + (1+q)\hat{k} \)
is \( \frac{\pi}{2} \)
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For angle between lines, use direction vectors and apply dot product condition.