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Given an equilateral triangle \( \mathrm{ABC} \) with side length equal to ' \( \mathrm{a} \) '. Let \( \mathrm{M} \) and \( \mathrm{N} \) be two
W points respectively on the side \( \mathrm{AB} \) and \( \mathrm{AC} \) such that \( \overline{\mathrm{AN}}=\mathrm{K} \overline{\mathrm{AC}} \) and \( \overline{\mathrm{AM}}=\frac{\overline{\mathrm{AB}}}{3} \). If \( \overline{\mathrm{BN}} \) and \( \overline{\mathrm{CM}} \) are orthogonal then the value of \( \mathrm{K} \) is equal to.
A \( \quad \frac{1}{5} \quad \) B \( \quad \frac{1}{4} \)
C \( \frac{1}{3} \)
D \( \frac{1}{2} \)
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