Mathematics

Problem

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

ABC

\cos 2A + \cos 2B + \cos 2C \ge -\frac{3}{2}

. Statement I is incorrect but Statement II is correct. Both Statement I and Statement II are correct. Statement I is correct but Statement II is incorrect. Both Statement I and Statement II are incorrect.

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