Calculate the angle between two 2D vectors using the dot product formula.
The angle between two vectors is the shortest angle at which one vector must be rotated about its tail to coincide with the other vector. It is always between 0 and 180 degrees (or 0 and π radians).
This calculation is fundamental in physics and engineering for determining the relationship between forces, velocities, and directions. If the angle is 90°, the vectors are orthogonal (perpendicular). If it's 0° or 180°, they are parallel.
Where A · B is the dot product and |A|, |B| are the magnitudes of the vectors.
The vectors are perpendicular (90°). This means they have no component in the same direction.
No, the angle between vectors is always defined as the non-negative shortest path between them (0° to 180°).
The vectors point in exactly opposite directions (antiparallel). This occurs when one vector is a negative multiple of the other.
The vectors point in the same direction (parallel). This occurs when one vector is a positive multiple of the other.
Radians are the standard unit in mathematics and physics. 1 radian ≈ 57.3°, and 2π radians = 360°.
The formula works in 3D and higher dimensions. Simply add the z-components to the dot product: (v1x*v2x + v1y*v2y + v1z*v2z).
The dot product (scalar product) of two vectors is the sum of the products of their corresponding components. It measures how much vectors align.
Magnitude (or length) of a vector is the distance from its origin to its endpoint, calculated as √(x² + y²) for 2D vectors.
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