A** vector** is a physical quantity that has a

Note:To study more about vectors, you can refer to this Answer.

In this Answer, we will discuss various types of vectors.

A **unit vector** is a vector with a magnitude of one. Any vector can become a unit vector by dividing it by the magnitude of the given vector. Suppose we have a vector

Here,

The following diagram helps us understand the unit vectors in three dimensions.

We represent the unit vector in the x-axis, y-axis, and z-axis with

Suppose we have a vector

Let's calculate its magnitude

$|v|$ :

We find the unit vector

$v̂$ using the formula we have studied above:

Now we find the magnitude of this unit vector

$|v̂|$ :

Hence, we prove the magnitude of a unit vector is 1.

A **zero vector** is a vector with a magnitude of zero. This means that the head and tail of the vector lie on the same point. We represent a zero vector as

For 2D space:

For 3D space:

Note:A zero vector has no direction.

A vector that gives the

Let's represent it graphically:

Suppose we have a vector

This vector indicates that we have moved 3 units to the right (in the x-direction) and 5 units upwards (in the y-direction) from point

A vector that gives information about the position of a vector with respect to

Let's represent it graphically:

Suppose we have a point

This position vector indicates that point

A vector in the opposite direction but having same magnitude as the original vector. Suppose we have a vector

Suppose we have a vector

Note:The coordinates of a negative vector are opposite in sign from the corresponding coordinates of the original vector.

Vectors that have the same starting point. Suppose we have two vectors:

Suppose we have two vectors

Vectors that have same the direction but not necessarily the same magnitude. Suppose we have two like vectors:

Suppose we have two vectors

Vectors that have different direction but not necessarily the same magnitude. Suppose we have two unlike vectors:

Suppose we have two vectors

Vectors that lie in the same plane. This means they can be positioned on the same surface without any of them extending out of that plane. Suppose we have two co-planar vectors:

Note:In a 2D space, any two vectors are always co-planar because they lie on the same flat plane.

Suppose we have two vectors

Vectors that are linear or parallel to each other. They can also have opposite directions, but they have to be parallel. They are also known as parallel vectors. Suppose we have two co-linear vectors:

Suppose we have two vectors

Note:Col-linear vectors are scalar multiples of each other, meaning one can be expressed as a linear combination of the other. The angle between these vector is$0^o$ .

Vectors that have same direction and magnitude. Suppose we have two equal vectors:

Suppose we have two vectors

Note:The x and y coordinates for two equal vectors are always same.

The vectors that are perpendicular to each other and have an angle of

Suppose we have two vectors

Vectors play a vital role in understanding the movement of objects around us. Each type of vector serves a distinct purpose. These types enable us to describe various relationships and phenomena in mathematics, physics, and various other disciplines of science.

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