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

If vec(x),vec(y) and vec(z) are non coplanar then prove that vec(x)+vec(y),vec(y)+vec(z) and vec(z)+vec(x) are non coplanar.

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

For vectors vec(a),vec(b) and vec( c ),vec(a).vec(b)=vec(a).vec( c ) and vec(a)xx vec(b)=vec(a)xx vec( c ),vec(a) ne vec(0) then show that vec(b)=vec( c ) .

Find |vec(a)| and |vec(b)| , if (vec(a)+vec(b)).(vec(a)-vec(b))=8 and |vec(a)|=8|vec(b)| .

The unit vectors vec(a),vec(b) and vec( c ) are not coplanar. If vec(a)xx(vec(b)xx vec( c ))=(1)/(sqrt(2))(b+c) then the angle between vec(a) and vec(b) is ………………

Let vec(a),vec(b) and vec( c ) be three unit vectors such that vec(a),+vec(b)+vec( c )=vec(0) . If lambda=vec(a)*vec(b)+vec(b)*vec( c )+vec( c )*vec(a) and vec(d)=vec(a)xx vec(b)+vec(b)xx vec( c )+vec( c )xx vec(a) then the ordered pair (lambda, vec(d)) is equal to :

The points A(vec(a)),B(vec(b)) and C(vec( c )) are collinear then ………….

Three vectors vec(a),vec(b) and vec( c ) satisfy the condition vec(a)+vec(b)+vec( c )=vec(0) . Evaluate the quantity mu=vec(a).vec(b)+vec(b).vec( c )+vec( c ).vec(a) , if |vec(a)|=1,|vec(b)|=4 and |vec( c )|=2 .

For three vectors vec(a),vec(b) and vec( c ),vec(a)+vec(b)+vec( c )=vec(0)|vec(a)|=3,|vec(b)|=4,|vec( c )|=5 , then evaluate 2(vec(a)*vec(b)+vec(b)*vec( c )+vec( c )*vec(a)) .