Zero vector or null vector is a vector
which has zero magnitude and an arbitrary direction. It is represented by . If a vector is
multiplied by zero, the result is a zero vector.
It is important to note that we cannot take the above result to be a number, the result has to be a vector and here lies the importance of
the zero or null vector. The physical meaning of can
be understood from the following examples.
The position vector of the origin of the coordinate axes is a zero vector.
The displacement of a stationary particle from time t to time tl is zero.
The displacement of a ball thrown up and received back by the thrower is a zero vector.
The velocity vector of a stationary body is a zero vector.
The acceleration vector of a body in uniform motion is a zero vector.
Properties of the zero vector
When a zero vector is added to another vector
,
the result is the vector
only.
Similarly, when a zero vector is subtracted from a vector
,
the result is the vector
.
When a zero vector is multiplied by a non-zero scalar, the result is a zero vector.
. If a vector is
multiplied by zero, the result is a zero vector.
The position vector of the origin of the coordinate axes is a zero vector.
The displacement of a stationary particle from time t to time tl is zero.
The displacement of a ball thrown up and received back by the thrower is a zero vector.
The velocity vector of a stationary body is a zero vector.
The acceleration vector of a body in uniform motion is a zero vector.
,
the result is the vector
When a zero vector is multiplied by a non-zero scalar, the result is a zero vector.
