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Show that the vectors -> a , -> band ...

Show that the vectors ` -> a , -> b`and ` -> c`coplanar if ` -> a+ -> b , -> b+ -> c`and ` -> c+ -> a`are coplanar

Text Solution

Verified by Experts

For `veca+vecb,vecb+vecc,vecc+veca`
to be coplanar, their scalar triple product must be zero.
Thus,`(veca+vecb)[(vecb+vecc) xx (vecc+veca)]=0`
⇒`(veca+vecb)[(vecb xx vecc) +(vecb xx veca)+(vecc xx vecc)+(vecc xx veca)]=0`
⇒`veca .(vecb xx vecc )+0+0+0+0+0+0+vecb ...
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