Let ` vec a , vec b ,a n d vec c` be any three vectors, then prove that `[ vec axx vec b vec bxx vec c vec cxx vec a]=[ vec a vec b vec c]^2dot`

If vec a , vec b ,a n d vec c are three vectors such that vec axx vec b= vec c , vec bxx vec c= vec a , vec cxx vec a= vec b , then prove that | vec a|=| vec b|=| vec c|dot

If vec a , vec b , vec c are any three noncoplanar vector, then the equaltion [ vec bxx vec c vec cxx vec a vec axx vec b]x^2+[ vec a+ vec b vec b+ vec c vec c+ vec a]x+1+[ vec b- vec c vec c- vec a vec a- vec b]=0 has roots a. real and distinct b. real c. equal d. imaginary

If vec aa n d vec b are two vectors, then prove that ( vec axx vec b)^2=| vec adot vec a vec adot vec b vec bdot vec a vec bdot vec b| .

Let vec a , vec b ,a n d vec ca n d vec a^' , vec b^' , vec c ' are reciprocal system of vectors, then prove that vec a^'xx vec b^'+ vec b^'xx vec c^'+ vec c^'xx vec a^'=( vec a+ vec b+ vec c)/([ vec a vec b vec c]) .

If vec a , vec b ,a n d vec c are three non-coplanar non-zero vecrtors, then prove that ( vec a . vec a) vec bxx vec c+( vec a . vec b) vec cxx vec a+( vec a . vec c) vec axx vec b=[ vec b vec c vec a] vec a

If vec a , vec ba n d vec c are three non coplanar vectors, then prove that vec d=( vec adot vec d)/([ vec a vec b vec c])( vec bxx vec c)+( vec bdot vec d)/([ vec a vec b vec c])( vec cxx vec a)+( vec cdot vec d)/([ vec a vec b vec c])( vec axx vec b)

If vec a , vec b , vec c ,a n d vec d are four non-coplanar unit vector such that vec d make equal angles with all the three vectors vec a , vec ba n d vec c , then prove that [ vec d vec a vec b]=[ vec d vec c vec b]=[ vec d vec c vec a]dot

If vectors vec a , vec b ,a n d vec c are coplanar, show that | vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=0

For any three vectors veca, vec b, vec c prove that (vec a + vec b)+ vec c = vec a + (vec b + vec c)

Prove that [ vec a, vec b, vec c + vec d] = [ vec a, vec b, vec c] + [ vec a, vec b , vec d] .