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.

vec(a) and vec(b) are any two vectors. Prove that |vec(a)+vec(b)|le|vec(a)|+|vec(b)|

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.

Show that, (vec(a)-vec(b))xx(vec(a)+vec(b))=2(vec(a)xx vec(b)) .

Let vec(A), vec(B) and vec(C) , be unit vectors. Suppose that vec(A).vec(B)=vec(A).vec(C)=0 and the angle between vec(B) and vec(C) is pi/6 then

vec(u),vec(v) and vec(w) are not co-planar vectors and p and q are real numbers. If [3vec(u),p vec(v),p vec(w)]-[p vec(v),vec(w),q vec(u)]-[2vec(w),q vec(v),q vec(u)]=0 then ……………

The position vectors of the points A, B, C are vec(a),vec(b) and vec( c ) respectively. If the points A, B, C are collinear then prove that vec(a)xx vec(b)+vec(b)xx vec( c )+vec( c )xxvec(a)=vec(0) .

The vectors vec(a) and vec(b) are not perpendicular. The vectors vec( c ) and vec(d) are such that vec(b)xx vec( c )=vec(b)xx vec(d) and vec(a).vec(d)=0 then vec(d) = ……………

Let vec(a),vec(b) and vec( c ) be unit vectors such that vec(a).vec(b)=vec(a).vec( c )=0 and the angle between vec(b) and vec( c ) is (pi)/(6) . Prove that vec(a)=+-2(vec(b)xx vec( c )) .

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 :

vec(a),vec(b) and vec( c ) are non zero vectors. (vec(a)xx vec(b))xx vec( c )=(1)/(3)|vec(b)||vec( c )|vec(a) . If the acute angle between the vectors vec(b) and vec( c ) is theta then sin theta = ……………