JEE Main 202122 Jul, Evening shiftMathematicsHardVector Algebra184× since 2002Let three vectors a→\overrightarrow aa, b→\overrightarrow bb and c→\overrightarrow cc be such that a→×b→=c→\overrightarrow a \times \overrightarrow b = \overrightarrow ca×b=c, b→×c→=a→\overrightarrow b \times \overrightarrow c = \overrightarrow ab×c=a and ∣a→∣=2\left| {\overrightarrow a } \right| = 2a=2. Then which one of the following is not true?AOption A. a→×((b→+c→)×(b→×c→))=0→\overrightarrow a \times \left( {(\overrightarrow b + \overrightarrow c ) \times (\overrightarrow b \times \overrightarrow c )} \right) = \overrightarrow 0a×((b+c)×(b×c))=0BOption B. Projection of a→\overrightarrow aa on (b→×c→)(\overrightarrow b \times \overrightarrow c )(b×c) is 2COption C. [a→b→c→]+[c→a→b→]=8\left[ {\matrix{ {\overrightarrow a } & {\overrightarrow b } & {\overrightarrow c } \cr } } \right] + \left[ {\matrix{ {\overrightarrow c } & {\overrightarrow a } & {\overrightarrow b } \cr } } \right] = 8[abc]+[cab]=8DOption D. ∣3a→+b→−2c→∣2=51{\left| {3\overrightarrow a + \overrightarrow b - 2\overrightarrow c } \right|^2} = 513a+b−2c2=51CheckSkip · show solution
