Answer to Question #96652 in Analytic Geometry for Manisha Nayak

Question #96652
Show that for any three vector a, b, c
a*(b*c)+b*(c*a) +c*(a*b) =0
1
Expert's answer
2019-10-17T11:24:46-0400

We have:

"\\bold{a\\times(b\\times c)=b(a\\cdot c)-c(a\\cdot b)}"

"\\bold{b\\times(c\\times a)=c(b\\cdot a)-a(b\\cdot c)}"

"\\bold{c\\times(a\\times b)=a(c\\cdot b)-b(c\\cdot a)}"

And


"\\bold{(a\\cdot c)=(c\\cdot a), (a\\cdot b)=(b\\cdot a), (b\\cdot c)=(c\\cdot b)}"

Thus,


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


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