Solve the vector equation in `vec(x): vec(x) + vec(x) xx vec(a) = vec(b)`.

For a non zero vector vec(A) . If the equations vec(A).vec(B) = vec(A).vec(C) and vec(A) xx vec(B) = vec(A) xx vec(C) hold simultaneously, then

Let vec(a), vec(b), vec(c) be three vectors mutually perpendicular to each other and have same magnitude. If a vector vec(r) satisfies vec(a) xx {(vec(r) - vec(b)) xx vec(a)} + vec(b) xx {(vec(r) - vec(c)) xx vec(b)} + vec(c) xx {(vec(r) - vec(a)) xx vec(c)} = vec(0) , then vec(r) is equal to :

If vec(a) and vec(b) are two unit vectors, then the vector (vec(a) + vec(b)) xx (vec(a) xx vec(b)) is parallel to

Given two orthogonal vectors vec(A) and vec(B) each of length unity . Let vec(P) be the vector satisfying the equation vec(P) xx vec(B) = vec(A) - vec(P) . Then (vec(P) xx vec(B)) xx vec(B) is equal to .

If vec(a), vec(b), vec(c ) are three vectors such that vec(a)xx vec(b)=vec(c ), vec(b)xx vec(c )=vec(a) , prove that vec(a), vec(b), vec(c ) are mutually at right angles and |vec(b)|=1, |vec(c )|=|vec(a)| .

Solve the simultaneous vector equation of vec x and vec y, vec x + vec c xxvec y = vec a, vec y + vec c xxvec x = vec b where vec c! = 0

Prove that for any two vectors vec(a) and vec(b), vec(a).(vec(a)xx vec(b))=0 . Is vec(b).(vec(a)xx vec(b))=0 ?

If vec(a) and vec(b) are two vectors then the value of (vec(a) + vec(b)) xx (vec(a) - vec(b)) is

Let three vectors vec(a), vec(b) and vec(c ) be such that vec(a) xx vec(b) = vec(c), vec(b) xx vec(c) = vec(a) and |vec(a)| = 2 . Then which one of the following is not true ?