GATE 2022 PI – Question 11
Engineering Mathematics · Linear Algebra · 1 mark · Multiple choice
For vectors a,b,c, find $(\mathbf a\times\mathbf b)\times\mathbf c$.
- $(\mathbf a\cdot\mathbf c)\mathbf b-(\mathbf a\cdot\mathbf b)\mathbf c$
- $(\mathbf a\cdot\mathbf b)\mathbf c-(\mathbf a\cdot\mathbf c)\mathbf b$
- $(\mathbf a\cdot\mathbf c)\mathbf b-(\mathbf b\cdot\mathbf c)\mathbf a$
- $(\mathbf b\cdot\mathbf c)\mathbf a-(\mathbf a\cdot\mathbf c)\mathbf b$
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Show answer and explanation
Correct answer: (C) $(\mathbf a\cdot\mathbf c)\mathbf b-(\mathbf b\cdot\mathbf c)\mathbf a$
Explanation
Use antisymmetry: $(a\times b)\times c=-c\times(a\times b)$. The vector triple-product identity gives $c\times(a\times b)=a(c\cdot b)-b(c\cdot a)$. Negating yields **(a·c)b−(b·c)a, C**.
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