Let Let be the vector such that and .Then is equal to:

Engineering

Mathematics

Scalar Triple Product

Question

Let $\vec{a} = \hat{i} + 2 \hat{j} + \hat{k}, \vec{b} = 3 (\hat{i} - \hat{j} + \hat{k})$ Let $\vec{c}$ be the vector such that $\vec{a} \times \vec{c} = \vec{b}$ and $\vec{a} . \vec{c} = 3$ .

Then $\vec{a} . ((\vec{c} \times \vec{b}) - \vec{b} - \vec{c})$ is equal to:

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$(\vec{a} \times \vec{c}) \vec{b} = \vec{b} . \vec{b}$

$[\vec{a} \vec{c} \vec{b}] = 9 (1 + 1 + 1) = 27$

$\vec{a} . \vec{b} = 3 (1 - 2 + 1) = 0 \Rightarrow \vec{a} . \vec{c} = 3$

$\vec{a} . ((\vec{c} \times \vec{b}) - \vec{b} - \vec{c}) = [\vec{a} \vec{c} \vec{b}] - \vec{a} . \vec{b} - \vec{a} . \vec{c}$

= 27 – 0 – 3 = 24