JEE Main 202324 Jan, Evening shiftMathematicsHardVector Algebra184× since 2002Let α→=4i^+3j^+5k^\overrightarrow \alpha = 4\widehat i + 3\widehat j + 5\widehat kα=4i+3j+5k and β→=i^+2j^−4k^\overrightarrow \beta = \widehat i + 2\widehat j - 4\widehat kβ=i+2j−4k. Let β→1{\overrightarrow \beta _1}β1 be parallel to α→\overrightarrow \alphaα and β→2{\overrightarrow \beta _2}β2 be perpendicular to α→\overrightarrow \alphaα. If β→=β→1+β→2\overrightarrow \beta = {\overrightarrow \beta _1} + {\overrightarrow \beta _2}β=β1+β2, then the value of 5β→2 .(i^+j^+k^)5{\overrightarrow \beta _2}\,.\left( {\widehat i + \widehat j + \widehat k} \right)5β2.(i+j+k) is :AOption A. 9BOption B. 7COption C. 6DOption D. 11CheckSkip · show solution
