Between the following two statements: Statement I : Let $\vec { a } = \hat { i } + 2 \hat { j } - 3 \hat { k }$ and $\vec { b } = 2 \hat { i } + \hat { j } - \hat { k }$. Then the vector $\vec { r }$ satisfying $\vec { a } \times \vec { r } = \vec { a } \times \vec { b }$ and $\vec { a } \cdot \vec { r } = 0$ is of magnitude $\sqrt { 10 }$. Statement II : In a triangle $A B C , \cos 2 A + \cos 2 B + \cos 2 C \geq - \frac { 3 } { 2 }$. (1) Statement I is incorrect but Statement II is correct. (2) Both Statement I and Statement II are correct. (3) Statement I is correct but Statement II is incorrect. (4) Both Statement I and Statement II are incorrect.
Between the following two statements: Statement I : Let $\vec { a } = \hat { i } + 2 \hat { j } - 3 \hat { k }$ and $\vec { b } = 2 \hat { i } + \hat { j } - \hat { k }$. Then the vector $\vec { r }$ satisfying $\vec { a } \times \vec { r } = \vec { a } \times \vec { b }$ and $\vec { a } \cdot \vec { r } = 0$ is of magnitude $\sqrt { 10 }$.\\
Statement II : In a triangle $A B C , \cos 2 A + \cos 2 B + \cos 2 C \geq - \frac { 3 } { 2 }$.\\
(1) Statement I is incorrect but Statement II is correct.\\
(2) Both Statement I and Statement II are correct.\\
(3) Statement I is correct but Statement II is incorrect.\\
(4) Both Statement I and Statement II are incorrect.