If vectors \( \vec{a} = 3\hat{i} + 2\hat{j} + \lambda\hat{k} \) and \( \vec{b} = 2\hat{i} - 4\hat{j} + 5\hat{k} \) represent the two strips of the Red Cross sign placed outside a doctor's clinic, then the value of \( \lambda \) is :
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Real-world application word cues like "Red Cross sign" or "orthogonal axes" indicate that the underlying angle is exactly \( 90^\circ \), meaning you should set the dot product equal to zero.