If the angle between the line \( 2(x + 1) = y = z \) and the plane \( 2x - y + \sqrt{2} z + 4 = 0 \) is \( \frac{\pi}{6} \), then the value of \( \lambda \) is:
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To find the angle between a line and a plane, use the formula:
\[
\cos \theta = \frac{|\vec{d} \cdot \vec{n}|}{|\vec{d}| |\vec{n}|}
\]
where \( \vec{d} \) is the direction vector of the line, and \( \vec{n} \) is the normal vector of the plane.