Between the following two statements: Statement I : Let $a = \hat{i} + 2 \hat{j} - 3 \hat{k}$ and $b = 2 \hat{i} + \hat{j} - \hat{k}$ . Then the vector $r$ satisfying $a \times r = a \times b$ and $a \cdot r = 0$ is of magnitude $10$ .
Statement II : In a triangle $A BC, cos 2 A + cos 2 B + cos 2 C \geq - \frac{3}{2}$ .

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​ a ˉ = i ^ + 2 j ^ ​ − 3 k ^ a ˉ = 2 i ^ + j ^ ​ − k ^ a ˉ × r ˉ = a ˉ × b ˉ ; a ˉ ⋅ r ˉ = 0 ⇒ a ˉ × ( r ˉ − b ˉ ) = 0 ⇒ a ˉ = λ ( r ˉ − b ˉ ) a ˉ ⋅ a ˉ = λ ( a ˉ ⋅ r ˉ − a ˉ ⋅ b ˉ ) 14 = − 7 λ ⇒ λ = − 2 2 − a ˉ ​ = r ˉ − b ˉ ⇒ r ˉ = b ˉ − 2 a ˉ ​ = 2 2 b ˉ − a ˉ ​ = 2 3 i ^ + k ^ ​ ​ Statement (I) is incorrect ​ cos 2 A + cos 2 B + cos 2 c ≥ − 2 3 ​ 2 A + 2 B + 2 C = 2 π cos 2 A + cos 2 B + cos 2 C = − 1 − 4 cos A ⋅ cos B ⋅ cos C ≥ − 1 − 4 × 2 1 ​ × 2 1 ​ × 2 1 ​ = − 2 3 ​ ​ Statement (II) is correct.

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