hexaedru8p

Answered

2022-10-09

If a and c are unit vectors at an angle $\pi /3$ with each other and $(a\times (b\times c)).(a\times c)=5$, then what is the value of [a b c]? I just know the basic meaning of what are vector and scalar triple product. How do I do this question?

Answer & Explanation

Salma Baird

Expert

2022-10-10Added 8 answers

We want to compute $a\cdot b\times c=-b\cdot a\times c$. We'll use $a\times (b\times c)=(a\cdot c)b-(a\cdot b)c$ so

$5=(a\times (b\times c))\cdot (a\times c)=(a\cdot c)(b\cdot a\times c).$

Hence

$[abc]=\frac{-5}{a\cdot c}=\frac{-5}{\mathrm{cos}\frac{\pi}{3}}=-10.$

Shawn Peck

Expert

2022-10-11Added 2 answers

Use $a\times (b\times c)=(a\cdot c)b-(a\cdot b)c$. Then

$(a\times (b\times c))\cdot (a\times c)=(a\cdot c)b\cdot (a\times c)-(a\cdot b)c\cdot (a\times c)=-(a\cdot b)[a,b,c]$

etc.

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