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Show that vectors vec a ,\ vec b ,\ v...

Show that vectors ` vec a ,\ vec b ,\ vec c` are coplanar if ` vec a+ vec b ,\ vec b+ vec c ,\ vec c+ vec 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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