The position vectors of the vertices \( A, B \) and \( C \) of a triangle are three unit vectors...

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The position vectors of the vertices \( A, B \) and \( C \) of a triangle are three unit vectors \( \hat{a}, \hat{b} \) and \( \hat{c} \), respectively. A vector \( \vec{d} \) is such that \( \vec{d} \cdot \hat{a}=\vec{d} \cdot \hat{b}=\vec{d} \cdot \hat{c} \) and \( \vec{d}=\lambda(\hat{b}+\hat{c}) \). Then triangle \( A B C \) is
(1) acute angled
(2) obtuse angled
(3) right angled
(4) none of these
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