(i) Equal vectors (ii) Like vectors (iii) Opposite vectors (iv) Unlike vectors (v) Unit vector and Orthogonal unit vectors (vi) Null vector or zero vector (vii) Proper vector (viii) Co-initial vectors (ix) Coplanar vectors

**Different types of vectors**

(i) Equal vectors

(ii) Like vectors

(iii) Opposite vectors

(iv) Unlike vectors

(v) Unit vector and Orthogonal unit vectors

(vi) Null vector or zero vector

(vii) Proper vector

(viii) Co-initial vectors

(ix) Coplanar vectors

**(i) Equal vectors**

Two vectors are said to be equal if they have the same magnitude and same direction, wherever be their

initial positions. In Fig. the vectors â†' A and â†' B have the same magnitude and direction. Therefore â†' A and â†' B are equal vectors.

*(ii) Like vectors*

Two vectors are said to be like vectors, if they have same direction but different magnitudes as shown in Fig. .

*(iii) Opposite vectors*

The vectors of same magnitude but opposite in direction, are called opposite vectors (Fig. ).

*(iv) Unlike vectors*

The vectors of different magnitude acting in opposite directions

are called unlike vectors. In Fig. the vectors A and B are unlike vectors.

*(v) Unit vector*

A vector having unit magnitude is called a unit vector. It is also defined as a vector divided by its own magnitude. A unit vector in the direction of a vector â†' A ,is written as Ã‚ and is read as 'A cap' or 'A caret' or 'A hat'. Therefore,

Thus, a vector can be written as the product of its magnitude and unit vector along its direction.

*Orthogonal unit vectors*

There are three most common unit vectors in the positive directions of X,Y and Z axes of Cartesian coordinate system, denoted by*i, j* and *k *respectively. Since they are along the mutually perpendicular directions,* *they are called orthogonal unit vectors.

*(vi) Null vector or zero vector*

A vector whose magnitude is zero, is called a null vector or zero vector. It is represented by 0 and its starting and end points are the same. The direction of null vector is not known.

*(vii) Proper vector*

All the non-zero vectors are called proper vectors.

**(viii) Co-initial vectors**

Vectors having the same starting point are called

co-initial vectors. In Fig. , â†' A and â†' B start from the same origin O. Hence, they are called as co-initial vectors.

*(ix) Coplanar vectors*

Vectors lying in the same plane are called coplanar vectors and the plane in which the vectors lie are called plane of vectors.

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11th 12th std standard Class Physics sciense Higher secondary school College Notes : Different types of vectors |

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