If `vec c` is normal to ` vec a` and `vec b`, show that `vec c`is normal to `vec a+ vec b` and `vec a - vec b`.

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 .

If vec axx vec b= vec cxxvec d and vec axx vec c= vec bxxvec d , show that vec a- vec d is parallel to vec b- vec c where vec a != vec d , vec b != vec c .

If ABCD is a parallelogram and vec AB = vec a , vec BC= vec b then show that vec AC = vec a+ vec b and vec BD = vec b- vec a .

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

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

If vec a is perpendicular to vec b and vec r is non-zero vector such that p vec r+( vec rdot vec a) vec b= vec c , then vec r= vec c/p-(( vec adot vec c) vec b)/(p^2) (b) vec a/p-(( vec cdot vec b) vec a)/(p^2) vec a/p-(( vec adot vec b) vec c)/(p^2) (d) vec c/(p^2)-(( vec adot vec c) vec b)/p

If vec c=3vec a+ 4vec b and 2vec c=vec a-vec 3b then show that vec c and vec a are like vectors and |quad vec c|>|quad vec a| .

If vec c= 3 vec a + 4 vec b and 2 vec c = vec a- 3 vec b , show that vec c and vec b have opposite directions and |quad vec c|> 2|quad vec b| .

If vec a , vec b and vec c are three vectors such that vec a+vec b+vec c=vec 0 , |quad vec a|=1 , |quad vec b|=4 and |quad vec c|=2 , then find the value of vec a.vec b+vec b.vec c+vec c.vec a .