# Angle Between Two Vectors Calculator

Vector is a quantity that has a magnitude and a direction. Vectors are used in GPS, generating weather reports etc., Here, the vectors are represented as a and B. This online calculator is used to find the angle formed between the two vectors. Enter the values of the both the vectors A and B, the angle formed between them will be displayed here.

Vector is a quantity that has a magnitude and a direction. Vectors are used in GPS, generating weather reports etc., Here, the vectors are represented as a and B. This online calculator is used to find the angle formed between the two vectors. Enter the values of the both the vectors A and B, the angle formed between them will be displayed here.

Code to add this calci to your website

#### Formula:

r = arccos ( ( a * x ) + ( b * y ) + ( c * z ) ) / ( √( a^{2} + b^{2} + c^{2}) * √( x^{2} + y^{2} + z^{2}) )
**Where,**
r = Angle Between Two vectors
a = i_{1} Co-efficient
b = j_{1} Co-efficient
c = k_{1} Co-efficient
x = i_{2} Co-efficient
y = j_{2} Co-efficient
z = k_{2} Co-efficient
### Example

#### Angle Between Two Vectors

**Consider the Vector A and B as 2i**_{1}+4j_{1}+6k_{1} and 1i_{2}+3j_{2}+5k_{2}, then

**Here**, a = 2, b = 4, c = 6 and x = 1, y = 3, z = 5

Cos(Angle) = ( ( 2 * 1 ) + ( 4 * 3 ) + ( 6 * 5 ) ) / ( √( 2^{2} + 4^{2} + 6^{2}) * √( 1^{2} + 3^{2} + 5^{2}) )

= ( 2 + 12 + 30 ) / ( √( 4 + 16 + 36 ) * √( 1 + 9 + 25 ) )

= ( 44 ) / ( √( 56 ) * √( 35 ) )

= 44 / ( 7.48* 5.92)

= 44 / 44.2816

= 0.994

Angle = arccos(0.994)

Angle = 6.28

Therefore, angle between two vectors is 6.28 Degrees or 0.11 radians.