MathematicsHard202×since 2002Q5852Between the following two statements: Statement I : Let a⃗=i^+2j^−3k^\vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}a=i^+2j^−3k^ and b⃗=2i^+j^−k^\vec{b}=2 \hat{i}+\hat{j}-\hat{k}b=2i^+j^−k^. Then the vector r⃗\vec{r}r satisfying a⃗×r⃗=a⃗×b⃗\vec{a} \times \vec{r}=\vec{a} \times \vec{b}a×r=a×b and a⃗⋅r⃗=0\vec{a} \cdot \vec{r}=0a⋅r=0 is of magnitude 10\sqrt{10}10. Statement II : In a triangle ABC,cos2A+cos2B+cos2C≥−32A B C, \cos 2 A+\cos 2 B+\cos 2 C \geq-\frac{3}{2}ABC,cos2A+cos2B+cos2C≥−23.ABoth Statement I and Statement II are correct.BBoth Statement I and Statement II are incorrect.CStatement I is correct but Statement II is incorrect.DStatement I is incorrect but Statement II is correct.Check answerSkip