JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumVector Algebra184× since 2002Let a→=2ı^−ȷ^+3k^\overrightarrow{\mathrm{a}}=2\hat{\imath}-\hat{\jmath}+3\hat{k}a=2^−^+3k^, b→=3ı^−5ȷ^+k^\overrightarrow{\mathrm{b}}=3\hat{\imath}-5\hat{\jmath}+\hat{k}b=3^−5^+k^ and c→\overrightarrow{\mathrm{c}}c be a vector such that a→×c→=c→×b→\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{b}}a×c=c×b and (a⃗+c⃗)⋅(b⃗+c⃗)=168(\vec{a}+\vec{c}) \cdot (\vec{b}+\vec{c})=168(a+c)⋅(b+c)=168. Then the maximum value of ∣c⃗∣2|\vec{c}|^2∣c∣2 is:AOption A. 462BOption B. 77COption C. 154DOption D. 308CheckSkip · show solution
