Define : (i) collinear vectors and (ii) coplanar vectors.

Given (i) Two vectors are said to be like vectors if they have opposite directions. (ii) Two unlike vectors have, opposite directions (iii) Like or unlike vectors are called collinear vectors. Then -

Column I, Column II Collinear vectors, p. vec a Coinitial vectors, q. vec b Equal vectors, r. vec c Unlike vectors (same intitial point), s. vec d

veca , vecb and vecc are three non-coplanar vectors and vecr . Is any arbitrary vector. Prove that [vecbvecc vecr]veca+[vecc veca vecr]vecb+[vecavecbvecr]vecc=[veca vecb vecc]vecr .

Define a vector and a unit vector. Find in terms of vector vec(a) a unit vector in its direction.

Answer the followings true or false. (i) vecaand-veca are collinear. (ii) Two collinear vectors are always equal in magnitude. (iii) Two vectors having same magnitude are collinear. (iv) Two collinear vectors having the same magnitude are equal.

Define position vector.

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.

Define scalar product of two vectors . Show of two vectors . Show that scalar product of vectors satisfies the commutative and distributive laws.

Define cloning vector. Give example.

If vec(a)=hat(i)+hat(j)-4hat(k) " and " vec(b)=4hat(i)-hat(j)-2hat(k) , then find (i) a unit vector in the direction of the vector (2vec(a)-vec(b)) and (ii) vector and scalar components of the vector (2vec(a)-vec(b)) along coordinate axes.