If `vec(a)=vec(OA) " and " vec(b)=vec(AB), " then " vec(a)+vec(b)` is -

ABCDEF is a regular hexagon. If vec(CD)=vec(a), vec(DE)=vec(b), " find " vec(AB), vec(BC), vec(BF), vec(CA), vec(AD) " and " vec(BD) in terms of vec(a) " and " vec(b) .

If |vec(a)|= |vec(b)| =1 and |vec(a) xx vec(b)|= vec(a).vec(b) , then |vec(a) + vec(b)|^(2)=

If (vec(a)-vec(b)).(vec(a)+vec(b))=27 and |vec(a)|=2|vec(b)| the find |vec(a)| and |vec(b)| .

For non-zero vectors vec(a) and vec(b), " if " |vec(a) + vec(b)| lt |vec(a) - vec(b)| , then vec(a) and vec(b) are-

If OACB is a parallelogramwith vec(OC) = vec a and vec (AB) = vec b, " then " vec(OA)=

If vec(a), vec(b) and vec(c) are three vectors such that vec(a) times vec(b)=vec(c) and vec(b) times vec(c)=vec(a)," prove that "vec(a), vec(b), vec(c) are mutually perpendicular and abs(vec(b))=1 and abs(vec(c))=abs(vec(a)) .

For the vector vec(a) and vec (b) if |vec(a) + vec(b)| = |vec(a) - vec(b)| , show that vec(a) and vec (b) are perpendicular

For the vectors vec(a) " and " vec(b) show that (i) abs(vec(a)+vec(b)) le abs(vec(a))+abs(vec(b)) " (ii) " abs(abs(vec(a))-abs(vec(b))) le abs(vec(a)-vec(b))

If abs(vec(a)+vec(b))=abs(vec(a)-vec(b)) , then show that vec(a) and vec(b) are perpendicular to each other.

If OACB is a parallelogrma with vec( OC) = vec(a) and vec( AB) = vec(b) then vec(OA) is equal to