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.

i1
j1
k1
i2
j2
k2

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.

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Formula:

r = arccos ( ( a * x ) + ( b * y ) + ( c * z ) ) / ( √( a2 + b2 + c2) * √( x2 + y2 + z2) ) Where, r = Angle Between Two vectors a = i1 Co-efficient b = j1 Co-efficient c = k1 Co-efficient x = i2 Co-efficient y = j2 Co-efficient z = k2 Co-efficient

Example

Angle Between Two Vectors

Consider the Vector A and B as 2i1+4j1+6k1 and 1i2+3j2+5k2, then

Here, a = 2, b = 4, c = 6 and x = 1, y = 3, z = 5
Cos(Angle) = ( ( 2 * 1 ) + ( 4 * 3 ) + ( 6 * 5 ) ) / ( √( 22 + 42 + 62) * √( 12 + 32 + 52) )
             = ( 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.

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