Unit Vector

About Unit Vector

A unit vector is one whose magnitude is equal to one. The "cap" symbol represents the unit vectors. Unit vectors have a length of one. Unit vectors are commonly used to indicate a vector's direction. A unit vector has the same direction as the given vector but a magnitude of one unit; for example, a unit vector for vector A is and = (1/|A|)

i, j, and k are unit vectors in directions of the x-axis, y-axis, and z-axis in a 3-dimensional plane. i.e. Get the List of all Maths formulas in one place.

1. |i| = 1
2. |j| = 1
3. |k| = 1

Vector’s Magnitude:

The numeric value of a vector is determined by its magnitude. A vector has both a magnitude and a direction. The magnitude of a vector formula is the sum of the vector's component measures along the x, y, and z axes. |A| is the magnitude of a vector A. The magnitude of a vector with the direction along the x-axis, y-axis, and z-axis can be calculated by taking the square root of the total of the square of its direction ratios. Let us begin by looking at the magnitude of a vector formula below.

For a vector A = ai + bj + ck its magnitude is: |A| =

Unit Vector Notation

Unit Vector is represented by ‘^’, which is called a cap, such as . It is given by = a/|a| Where |a| is for norm or magnitude of vector a.

Unit Vector Formula

An arrow signifies a unit vector because vectors have both magnitude (Value) and direction (Direction). We divide every vector's magnitude by its unit vector to determine its unit vector. Any vector is usually represented by the coordinates x, y, and z.

There are two ways to express a vector:

1. a = (x, y, z) using the brackets.
2. a = xi + yj +zk

The formula for determining a vector's magnitude is: |a| =

The formula of the unit vector in the direction of a given vector is:

Unit Vector = Vector/Vector's magnitude

How to find the unit vector?

Simply divide a given vector by its magnitude to find a unit vector with the same direction. Take, for example, the vector v = (3, 4) with the magnitude |v|. We may derive the unit vector by dividing each component of vector v by |v|, which is in the same direction as v.

|v| = = 5

Thus, = v / |v| = (3, 4) / 5 = (3/5, 4/5).

Vectors Properties

The properties of vectors are helpful to gaining a detailed understanding of vectors and also in performing numerous calculations involving vectors, A few important properties of vectors are listed here.

1. A . B = B. A
2. A × B ≠ B × A
3. i. i = j . j = k . k = 1
4. i . j = j . k = k . i = 0
5. i × i = j × j = k × k = 0
6. i × j = k; j × k = i; k × i = j
7. j × i = -k; k × j = -i; i × k = -j

• The dot product of two vectors is a scalar that resides in the plane of the two vectors.
• The cross product of two vectors is a vector perpendicular to the plane containing these two vectors