Between the following two statements: Statement I: Let a=i+2 j-3 k and b=2 i+j-k. Then the vector r satisfying a × r=a × b and a · r=0 is of magnitude √(10). Statement II: In a triangle A B C, cos 2 A+ cos 2 B+ cos 2 C ≥-3/2.

(D) Statement I is incorrect but Statement II is correct.

(A) Both Statement I and Statement II are correct.

(B) Both Statement I and Statement II are incorrect.

(C) Statement I is correct but Statement II is incorrect.

Vector Algebra: JEE Main 2024 Mathematics question

JEE Main 2024 · 9 Apr, Evening shift · Q5852

JEE Main 20249 Apr, Evening shiftMathematicsHardVector Algebra184× since 2002

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}