If `vec(a)+5vec(b)=vec(c )` and `vec(a)-7vec(b)=2vec(c )`, then show that `vec(a)` has the same direction as that of `vec(c )` and opposite direction to that of `vec(b)`.

If vec(a)=vec(b)+vec(c ) , then |vec(a)|=|vec(b)+vec(c )| .

If vec c=3vec a+4vec b and 2vec c=vec a-3vec b show that (i)vec c and vec a have the same direction and |vec c|>|vec a|(ii)vec b and vec c have opposite direction and |vec c|>|vec b|

If |vec a|+|vec b|=|vec c| and vec a+vec b=vec c, then find the angle between vec a and vec b

[vec(a)vec(b)vec(c )]=[vec(b)vec(c )vec(a)]=[vec(c )vec(a)vec(b)] .

If vec( A) + vec(B) =vec( C ) , and | vec(A)| =2 | vec( B) | and vec( B). vec( C ) = 0 , then

If vec(a)+vec(b)+vec(c )=0 " and" |vec(a)|=3,|vec(b)|=5, |vec(c )|=7 , then find the value of vec(a),vec(b)+vec(b).vec(c )+vec(c ).vec(a) .

If |vec a|=3,|vec b|=5,|vec c|=7 and vec a+vec b+vec c=0 then angle between vec a and vec b is

If vec(a), vec(b), vec(c ) are three vectors such that vec(a)+vec(b)+vec(c )=0 , then prove that : vec(a)xx vec(b)=vec(b)xx vec(c )=vec(c )xx vec(a) and hence, show that [vec(a)vec(b)vec(c )]=0 .

If the vectors vec(a), vec(b) and vec(c ) satisfy the condition vec(a)+vec(b)+vec(c )=vec(0) and |vec(a)|=3, |vec(b)| =4 and |vec(c )|=5 , then show that vec(a).vec(b)+vec(b).vec(c )+vec(c ). vec(a)=-25 .