Expression of a non-zero vector `vec r` as a linear combination of a non-zero vector `vec a` which is non-collinear with `vec r` and another vector perpendicular to `vec a` and coplanar with `vec r and veca` is given as

If a vector vec a is perpendicular to two non-collinear vector vec b and vec c , then vec a is perpendicular to every vector in the plane of vec b and vec c .

If a vector vec a is perpendicular to two non- collinear vector vec b and vec c ,then vec a is perpendicular to every vector in the plane of vec b and vec c.

If vec(a) is a non-zero vector and m is a non-zero scalar, then m vec(a) is a unit vector if

If a vector vec a is perpendicular to two non coplasnar vectors vec b and vec c ,then vec a is perpendicular to every vector in the plane of vec b and vec .

If vec b is a non-zero vector, then projection of vec a on vec b is

Let vec a, vec b and vec c be three non zero vectors such that no two of these are collinear. If the vector vec a + 2 vec b is collinear with vec c and vec b + 3 vec c is collinear with vec a then vec a + 2 vec b + 6 vec c =

Three non-zero vectors vec(a), vec(b), vec(c) are such that no two of them are collinear. If the vector (vec(a)+vec(b)) is collinear with the vector vec(c) and the vector (vec(b)+vec(c)) is collinear with vector vec(a) , then prove that (vec(a)+vec(b)+vec(c)) is a null vector.

vec a,vec b and vec c are three non-zero vectors,no two of which are collinear and the vectors vec a+vec b is collinear with vec b,vec b+vec c is collinear with vec a, then vec a+vec b+vec c=

Let vec a,vec b,vec c be three non-zero vectors such that any two of them are non-collinear.If vec a+2vec b is collinear with vec c and vec b+3vec c is collinear with vec a then prove that vec a+2vec b+6vec c=vec 0