jee-main 2024 Q78

jee-main · India · session1_27jan_shift1 Vectors: Cross Product & Distances
If $\vec { a } = \hat { i } + 2 \hat { j } + \hat { k } , \vec { b } = 3 ( \hat { i } - \hat { j } + \hat { k } )$ and $\overrightarrow { \mathrm { c } }$ be the vector such that $\vec { a } \times \vec { c } = \vec { b }$ and $\vec { a } \cdot \vec { c } = 3$, then $\vec { a } \cdot ( ( \vec { c } \times \vec { b } ) - \vec { b } - \vec { c } )$ is equal to
(1) 32
(2) 24
(3) 20
(4) 36
If $\vec { a } = \hat { i } + 2 \hat { j } + \hat { k } , \vec { b } = 3 ( \hat { i } - \hat { j } + \hat { k } )$ and $\overrightarrow { \mathrm { c } }$ be the vector such that $\vec { a } \times \vec { c } = \vec { b }$ and $\vec { a } \cdot \vec { c } = 3$, then $\vec { a } \cdot ( ( \vec { c } \times \vec { b } ) - \vec { b } - \vec { c } )$ is equal to\\
(1) 32\\
(2) 24\\
(3) 20\\
(4) 36