|In the following figure, identify co-initial, equal, collinear and negative vectors.
|Sol: In the given figure,
Co-initial vectors: , , , , and .
Equal vectors: and .
Collinear vectors:, ;, ; , ; , ; , .
Negative vectors: and ; and .
Types of Vectors
Zero vector: A vector whose initial and terminal points coincide, is called a zero vector or null vector. In other words, a vector that has zero magnitude is called a zero vector. It is denoted by or , , etc. The direction of the zero vector is indeterminate.
Unit vector: A vector whose magnitude is 1 unit (i.e., unity) is called a unit vector. The unit vector in the direction of a given vector is represented by and read as 'b cap' or 'b hat'.
The only purpose of unit vectors is to describe the direction. In Cartesian coordinate system, , and are the unit vectors that point along the x, y and z-axes respectively.
Co-initial vectors: The vectors having the same initial point are called co-initial vectors.
Collinear vectors: Two or more vectors are said to be collinear if they are parallel to each other, irrespective of their magnitudes and directions.
Equal vectors: Two vectors and are said to be equal, if they have the same magnitude (i.e., || = ||) and direction regardless of whether they have the same initial points or not. If and are equal vectors, then = .
Negative of a vector: A vector having same magnitude but in the opposite direction to a given vector is called the negative vector. For example, vector is negative of the vector and written as: = – . In order to find the negative of a vector, we merely reverse its arrowhead (direction).