Show that vectors ` vec a ,\ vec b ,\ vec c` are coplanar if ` vec a+ vec b ,\ vec b+ vec c ,\ vec c+ vec a` are coplanar.

Prove that [vec a -vec b, vec b - vec c, vec c- vec a] =0

If the vectors vec a, vec b, vec c are coplanar then (vec a xx vec b)* vec c = (vec b xx vec c)*vec a =...........

For any three vectors vec a,vec b and vec c , show that vec a- vec b,vec b- vec c and vec c- vec a are coplanar.

If vec a , vec b and vec c are non-coplanar (independent) vectors, prove that the vectors vec a- 2 vec b+ 3 vec c , -2 vec a + 3 vec b- 4 vec c and vec a -vec b+ 2 vec c are also linearly independent.

Prove that [vec a+ vec b, vec b +vec c, vec c + vec a]= 2 [vec a vec b vec c]

If vec a+ vec b + vec c= 0 , show that vec axxvec b= vec bxx vec c= vec cxx vec a .

Show that the points with position vectors vec a- 2 vec b+ 3 vec c , -2 vec a + 3 vec b+ 2 vec c and -8 vec a + 13 vec b are collinear, whatever vec a , vec b and vec c may be.

A,B,C and D are four points with position vectors vec a , vec b , vec c and vec d respectively such that 5 vec a - 2 vec b + 6 vec c- 9 vec d= vec 0 . Show that the point A,B,C,D are coplanar and find find the P.V. of the point in which the lines AC and BD intersects.

For any three vectors a ,\ b ,\ c prove that [ vec a+ vec b\ , vec b+ vec c\ , vec c+ vec a]=2\ [ vec a\ vec b\ vec c]dot

If A,B,C,D are the points with position vectors vec a , vec b , 3 vec a+ 2 vec b and vec a- 2 vec b respectively , show that vec AC = 2 vec a + 2 vec b and vec DB= 3 vec b - a .