When using an arrow to represent velocity, the length of the arrow stands for speed, and the way the arrow points indicates the direction.

Explanation: The length of a vector is also know as the magnitude. The magnitude determines how quickly something is moving through space whereas the direction tells you where the vector is going.

In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space….Examples

• A vector field for the movement of air on Earth will associate for every point on the surface of the Earth a vector with the wind speed and direction for that point.
• Velocity field of a moving fluid.

In my opinion both are almost same. However there should be some differenes like any two elements can be multiplied in a field but it is not allowed in vector space as only scalar multiplication is allowed where scalars are from the field. Every field is a vector space but not every vectorspace is a field.

Vector fields have many important applications, as they can be used to represent many physical quantities: the vector at a point may represent the strength of some force (gravity, electricity, magnetism) or a velocity (wind speed or the velocity of some other fluid).

We can have a constant vector field, meaning at each position the vector is the same. But in general a vector field can have an arbitrary value for the vector at every position. Acceleration is a vector; it has a magnitude and direction in three space.

In vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a transverse vector field) is a vector field v with divergence zero at all points in the field: A common way of expressing this property is to say that the field has no sources or sinks.

1a : a quantity that has magnitude and direction and that is commonly represented by a directed line segment whose length represents the magnitude and whose orientation in space represents the direction broadly : an element of a vector space. b : a course or compass direction especially of an airplane.

A unit vector is any vector that has a magnitude equal to one. Magnitude is a word that means length of a vector. So, any vector that has a length equal to one is a unit vector. Symbolically, it is written like this: |v| means the magnitude of v.

Vectors are the physical quantities that have magnitude, answering how much; as well as direction, answering where to. For example: implies displacement of towards . A unit vector is a type of vectors such that the magnitude of it is one unit. For example: implies unit displacement towards .

In mathematics, a set B of vectors in a vector space V is called a basis if every element of V may be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B.

(b) Unit vector has a magnitude equal to 1. ∴ Opition (b ) is the correct answer.

Now as we know a unit vector is a vector whose magnitude is unity (equal to 1) so we will check whose magnitude is unity and give the final answer. ⇒ It is Not a unit vector. It is a unit vector. Now, since Option 3 is NOT a unit vector we get OPTION C as the final answer.

From Wikipedia, the free encyclopedia. In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or “hat”, as in. (pronounced “v-hat”).

For example, displacement, velocity, and acceleration are vector quantities, while speed (the magnitude of velocity), time, and mass are scalars. To qualify as a vector, a quantity having magnitude and direction must also obey certain rules of combination.

Physical quantities specified completely by giving a number of units (magnitude) and a direction are called vector quantities. Examples of vector quantities include displacement, velocity, position, force, and torque.

A quantity that has magnitude but no particular direction is described as scalar. A quantity that has magnitude and acts in a particular direction is described as vector.