# Angle between Two Vectors Formula

## Angle between Two Vectors Formula

The Angle between Two Vectors Formula defines the distance between them. It can be discovered using either the cross product or the dot product (scalar product) (vector product). The   Angle between Two Vectors Formula vectors always ranges from 0° to 180°, as one should be aware.

An arrow that parallels the vector’s direction is used to indicate a vector.

If a vector is sent parallel to itself, nothing changes.

Parallel vectors are two vectors that have the same axis.

Anti-parallel vectors are two vectors with opposing directions.

Equal vectors are two vectors with the same magnitude and direction.

Negative vectors are two vectors with the same magnitude but in opposing directions.

### Concept of Vectors

Vectors are two-dimensional geometrical objects with magnitude and direction. A vector is represented as a line by an arrow pointing in that direction; the length of the line represents the magnitude of the vector. As a result, vectors are represented as arrows with starting and terminal points. Over 200 years, the idea of vectors evolved. Physical quantities such as displacement, velocity, and acceleration are represented by vectors.

The dot product formula may be used to compute the Angle between Two Vectors Formula. Consider two vectors, a and b, and their angle. ab = |a||b| cos gives the dot product of two vectors.The angle’s value must be determined. The angle formed by two vectors also reveals their orientations. To learn the Angle between Two Vectors Formula, students must visit the Extramarks website.

It can be evaluated using the following formula θ = cos-1[(a·b)/|a||b|]

Vectors can be subjected to many mathematical operations, such as addition, subtraction, and multiplication. Students will look at vector formulae for vector addition, subtraction, dot-product, cross-product, and  the Angle between Two Vectors Formula in this section.

Some fundamental vector operations can be done geometrically without the need for a coordinate system. These vector operations are represented by scalar addition, subtraction, and multiplication. In addition, there are two methods for multiplying two vectors together: the dot product and the cross product.

Subtraction of Vectors

Scalar Multiplication

Scalar Triple Product of Vectors

Multiplication of Vectors

### The Formula for the Angle between Two Vectors

The angle formed by two vectors is the angle formed by their tails. The cross product or the dot product (a scalar product) can be used to find it (vector product). It should be noted that the angle formed by two vectors is always between 0° and 180°. The angle generated by the intersection of two vectors’ tails is defined as the angle between them. If the vectors are not united tail-to-tail, students must join them tail-to-tail by parallel shifting one of the vectors. Here are a few examples of how to calculate the Angle between Two Vectors Formula.

There are two formulas for calculating theAngle between Two Vectors Formula one using the dot product and the other using the cross product. However, the dot product is used in the most frequent formula for calculating the Angle between Two Vectors Formula (see what the problem with the cross product is in the next section). Assume that the angle between the two vectors a and b is one. Then, using both dot product and cross product, below are the formulas for calculating the angle between them:

The Angle between Two Vectors Formula using dot product is  θ = cos-1 [ (a · b) / (|a| |b|) ]

The  Angle between Two Vectors Formula  using the cross product is  θ = sin-1 [ |a × b| / (|a| |b|) ]

### Solved Examples for Angle between Two Vectors Formula

1  Using one of the trigonometric equations for obtaining angles, determine the angle at vertex B of the given triangle.

BC = 3 units = Adjacent side of θ.

AC = 4 units = Opposite side of θ.

Students in this case understand both the opposite and adjacent sides of. As a result, they can use the tangent formula to determine.

⇒ tan θ = opposite side/adjacent side

⇒ tan θ = 4/3

⇒ θ = tan-1 (4/3) ⇒ θ = 53.1°

Hence, the angle at vertex B is 53.1°.