Test Academy | For three vectors A → = 2 j ^ − 3 k ^ , B → = − 2 i ^ + k ^ a n d C ^ = 3 i ^ − j ^ , where î, ĵ and k̂ are unit vectors along the axes of a right-handed rectangular/Cartesian coordinate system, the value of ( A . → ( B → × C → ) + 6 ) is

Question

For three vectors $\vec{A} = 2 \hat{j} - 3 \hat{k}, \vec{B} = - 2 \hat{i} + \hat{k} a n d \hat{C} = 3 \hat{i} - \hat{j},$ where î, ĵ and k̂ are unit vectors along the axes of a right-handed rectangular/Cartesian coordinate system, the value of $(\vec{A .} (\vec{B} \times \vec{C}) + 6)$ is

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Answer :

Correct answer is : 6

$\vec{A} = 2 \hat{j} - 3 \hat{k}, \vec{B} = - 2 \hat{i} + \hat{k} a n d \hat{C} = 3 \hat{i} - \hat{j}$

⇒ $\vec{A .} (\vec{B} \times \vec{C}) = | \begin{matrix} 0 & 2 & - 3 \\ - 2 & 0 & 1 \\ 3 & - 1 & 0 \end{matrix} |$

⇒ $\vec{A} (\vec{B} \times \vec{C}) = (- 2) (- 3) - 3 (2)$

⇒ $\vec{A .} (\vec{B} \times \vec{C}) = 0$

∴ $\vec{A .} (\vec{B} \times \vec{C}) + 6 = 6$

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