Acute angle between two vectors calculator

Angle Between Two Vectors Calculator to find the angle between two vector components. The concept of the vector angle is used to describe the angle difference of physical quantities which have a magnitude and a direction associated with them. The vector angle is calculated from the endpoint of the first line to the endpoint of the second line. The endpoint is determined by the vector direction in which the line was measured.

This calculator finds the angle between two vectors given their coordinates. The formula and the explanation can be found below the calculator.

Finding the angle between two vectors

We will use the geometric definition of the Dot product to produce the formula for finding the angle.

Geometrically the dot product is defined as

thus, we can find the angle as

To find the dot product from vector coordinates, we can use its algebraic definition.

Thus, for two vectors,

This is the formula used by the calculator.

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Find the vector angle with the x-axis step-by-step

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