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If the vectors vec a , vec b ,a n d vec...

If the vectors ` vec a , vec b ,a n d vec c` form the sides`B C ,C Aa n dA B ,` respectively, of triangle `A B C ,t h e n` (a)` vec adot vec b+ vec bdot vec c+ vec c dot vec a=0` (b)` vec axx vec b= vec bxx vec c= vec cxx vec a` (c). ` vec adot vec b= vec bdot vec c= vec c dot vec a` (d). ` vec axx vec b+ vec bxx vec c+ vec cxx vec a=0`

A

`vec(a).vec(b)+vec(b).vec(c)+vec(c).vec(a)=0`

B

`vec(a)xxvec(b)=vec(b)xxvec(c)=vec(c)xxvec(a)`

C

`vec(a).vec(b)=vec(b).vec(c)=vec(c).vec(a)`

D

`vec(a)xxvec(b)+vec(b)xxvec(c)+vec(c)xxvec(a)=vec(0)`

Text Solution

Verified by Experts

The correct Answer is:
B
Area of triangle `=1/2 (vec(a)xxvec(b))=1/2(bxxvec(c))=1/2(vec(c)xxvec(a))`
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