If a → = i ^ + j ^ + k ^ , b → =2 i ^ +λ+ k ^ , c → = i ^ − j ^ +4 k ^ and a → .( b → × c → )=10, then λ is equal to

Correct answer: (A) 6. 1 1 1 2 λ 1 1 -1 4 =10 14λ+1-18-1+1-2-λ=10 ⇒ 4λ+1-7-2-λ=10 ⇒ 3λ=18 ⇒ λ=6

Q97 / 150 · MHT CET 2016 · Mathematics

If $\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = 2 \hat{i} + λ + \hat{k}, \vec{c} = \hat{i} - \hat{j} + 4 \hat{k}$ and $\vec{a} . (\vec{b} \times \vec{c}) = 10,$ then $λ$ is equal to

|\begin{matrix} 1 & 1 & 1 \\ 2 & λ & 1 \\ 1 & - 1 & 4 \end{matrix}| = 10

1 (4 λ + 1) - 1 (8 - 1) + 1 (- 2 - λ) = 10

\Rightarrow 4 λ + 1 - 7 - 2 - λ = 10

\Rightarrow 3 λ = 18

\Rightarrow λ = 6

Hence, the correct answer is option: 'A'.