Show that for any three vectors `veca , vec b and vec c [ vec a + vec b, vecb + vec c , vec c + vec a ] =2[vec a , vec b , vecc]` .

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

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

For any three vectors vec a, vec b , vec c , show that vec a xx (vec b + vec c) + vec b xx (vec c + vec a) + vec c xx (vec a + vec b) = 0

Prove that if the vectors vec a, vec b, vec c satisfy vec a+ vec b + vec c = vec 0 , then vec bxx vec c = vec c xx vec a = vec a xx vec b

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

Let vec r be a non-zero vector satisfying vec r . vec a= vec r . vec b= vec r . vec c=0 for given non-zero vectors vec a , vec ba n d vec cdot Statement 1: [ vec a- vec b vec b- vec c vec c- vec a]=0 Statement 2: [ vec a vec b vec c]=0

For any two vectors veca and vec b show that |vec a. vec b| le |vec a||vec b| .

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

For any vectors vec a vec b , show that |vec a + vec b| le |vec a| + |vec b| .

Prove that vec a xx (vec b + vec c) + vec b xx(vec a + vec c)+ vec c xx(vec a + vec b) = vec 0