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Show that the vectors a , …

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

Posted by Harsh Gupta 5 years, 10 months ago

CBSE > Class 12 > Mathematics

1 answers

Shubham Negi 5 years, 10 months ago

Given [a+b,b+c,c+a]=0 this implies (a+b)•{(b+c)×(c+a)}=0 (a+b){(b×c)+(b×a)+(c×c)+(c×a)}=0 (a+b){(b×c)-(a×b)+0+(c×a)}=0 a(b×c)-a(a×b)+a(c×a)+b(b×c)-b(a×b)+b(c×a)=0 [a,b,c]-[a,a,b]+[a,c,a]+[b,b,c]-[b,a,b]+[b,c,a]=0 [a,b,c]-0+0+0-0+[a,b,c]=0 2[a,b,c]=0 [a,b,c]=0 Hence vector a b and c is coplanar

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