Question

What is a null vector, give example?

Answer 1

Hint: We know that a vector is a physical quantity which has both magnitude and direction. Thus clearly vectors can also have a value like zero. Then, such a vector is called a null vector. The null vector can be formed due to various cases as discussed below.

Complete answer:
We know that mathematical operations like addition, subtraction, multiplication and division can be carried out on vectors. We also know that two vectors can be added by vector addition. We also know that the direction of this resultant vector, formed due to vector addition is given by the phase diagram. Then, clearly, we can say that when two vectors of same magnitude and opposite direction act on the same body, then the resultant of the two vectors will be a null vector. This null vector will have zero magnitude and no direction.
 A real life example would be, two people pushing the cars in opposite directions with the same or equal force, or two people pulling a rope from opposite sides with the same or equal forces.
Similarly, a null vector can also be formed, when a zero scalar is multiplied with a non-zero vector, then from scalar multiplication, we can say that the resultant vector formed will be a null vector, with magnitude zero, and no direction.
An example would be work done by women standing at the same place, by holding a basket over her head.

Note:
We can also say that a null vector is a point with no direction or magnitude, thus we can represent a null vector by a point in a 3D space. Clearly, null vectors are formed due to the resultant of two or more vectors in different directions. Or by scalar multiplication by a zero scalar.