GATE CE 2024 Set 2 — Question 44

MSQ+2 / -0MediumVector IdentitiesVector CalculusEngineering Mathematics

Engineering Mathematics → Vector Calculus → Vector Identities

Last updated 5 September 2026

Question

\vec{p}

Your answer

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\vec{p} \times (\vec{q} \times \vec{r}) + \vec{q} \times (\vec{r} \times \vec{p}) + \vec{r} \times (\vec{p} \times \vec{q}) = \vec{0}

\vec{p} \times (\vec{q} \times \vec{r}) = (\vec{p} \cdot \vec{r}) \vec{q} - (\vec{p} \cdot \vec{q}) \vec{r}

\vec{p} \times (\vec{q} \times \vec{r}) = (\vec{p} \times \vec{q}) \times \vec{r}

\vec{r} \cdot (\vec{p} \times \vec{q}) = (\vec{q} \times \vec{p}) \cdot \vec{r}

The solution stays hidden until you check.

\vec{a} \times (\vec{b} \times \vec{c}) + \vec{b} \times (\vec{c} \times \vec{a}) + \vec{c} \times (\vec{a} \times \vec{b}) = \vec{0}

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\vec{a} \times (\vec{b} \times \vec{c}) + \vec{b} \times (\vec{c} \times \vec{a}) + \vec{c} \times (\vec{a} \times \vec{b}) = \vec{0}

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