If `vec a+vec b+vec c=0`, prove that `(vec a xx vec b)=(vec b xx vec c)=(vec c xx vec a)`

If veca , vec b , vec c are three vectors such that veca+ vec b+ vec c= vec0 , then prove that vec axx vec b= vec bxx vec c= vec cxx vec a

If 4 vec a+5 vec b+9 vec c=0, then ( vec axx vec b)xx[( vec bxx vec c)xx( vec cxx vec a)] is equal to a vector perpendicular to the plane of a ,b ,c b. a scalar quantity c. vec0 d. none of these

Prove that: ( vec a- vec b)*{( vec b- vec c)xx(vec c- vec a)}"=0

Prove that ( vec a- vec b)dot{( vec b- vec c)xx( vec c- vec a)}=0

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

Let vec a , vec b ,a n d vec c be non-coplanar vectors and let the equation vec a^' , vec b^' , vec c ' are reciprocal system of vector vec a , vec b , vec c , then prove that vec axx vec a^'+ vec bxx vec b^'+ vec cxx vec c ' is a null vector.

If veca , vec b and vec c represents three sides of a triangle taken in order prove that veca xx vec b = vec b xx vec c = vec c xx vec a

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

Let vec a , vec ba n d vec c be three non-coplanar vecrors and vec r be any arbitrary vector. Then ( vec axx vec b)xx( vec rxx vec c)+( vec bxx vec c)xx( vec rxx vec a)+( vec cxx vec a)xx( vec rxx vec b) is always equal to [ vec a vec b vec c] vec r b. 2[ vec a vec b vec c] vec r c. 3[ vec a vec b vec c] vec r d. none of these

Let the pairs a , b,and c ,d each determine a plane. Then the planes are parallel if a. ( vec axx vec c)xx( vec bxx vec d)= vec0 b. ( vec axx vec c).( vec bxx vec d)= vec0 c. ( vec axx vec b)xx( vec cxx vec d)= vec0 d. ( vec axx vec b).( vec cxx vec d)= vec0