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What is an equal vector and null vector?

Last updated date: 13th Aug 2024
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Answer
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Hint: Learn the definition in the theory part of vectors. Remember both are different. Vector is a line having direction and magnitude.

Complete step-by-step answer:
In the question we are asked what is an equal vector and null vector.
At first we will know what the vector is, then we will try to define an equal and null vector.
In mathematics and physics, a vector is an element of a vector space.
For many specific vector spaces, the vectors have received specific names which are listed below.

In classical Euclidean geometry (that is synthetic geometry), vectors were introduced as equivalence classes, under equipollence of ordered pairs of points; two pairs $\left( A,B \right)$ and $\left( C,D \right)$ being equipollent if the points $\left( A,B,D,C \right)$ in this order form a parallelogram such an equivalence class is called vector, more precisely a Euclidean vector. The equivalence class of $\left( A,B \right)$ is often denoted as $\overrightarrow{AB}$ .
A Euclidean vector is thus an entity endowed with a magnitude (the length of the line segment $\left( A,B \right)$) and a direction (the direction from $A$ to $B$). In physics, Euclidean vectors are used to represent physical quantities that have both magnitude and direction, but are located not at a specific place in contrast to scalars, which have no direction. For example velocity, acceleration and forces are vectors.
In the question the equal vectors are vectors that have the same magnitude and the same direction. Equal vectors may start at different positions.
The null vector is a vector having magnitude equal to zero. A null vector has no direction or it may have any direction. Generally a null vector is resultant of two equal vectors in opposite directions.

Note: Students should have thorough knowledge of theory behind vectors and should be familiar with theory behind it.
Students generally make mistakes in stating the definition. They sometimes state equal vectors are two vectors with only the same magnitude. This is totally wrong. They have the same direction too.
Similarly, in null vectors they get confused thinking how the magnitude can be zero, and hence they state null vectors as vectors with null direction. This is also wrong.