# Angle between vectors

Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)

Result

A =  0 °

#### Solution:

$u = \sqrt{ (-22)^{ 2 }+11^{ 2 } } = 11 \ \sqrt{ 5 } \doteq 24.5967 \ \\ v = \sqrt{ 16^{ 2 }+20^{ 2 } } = 4 \ \sqrt{ 41 } \doteq 25.6125 \ \\ s = (-22) \cdot \ (16)+(11) \cdot \ (20) = -132 \ \\ A = \frac{ 180^\circ }{ \pi } \cdot \arccos(s/(u \cdot \ v)) = \frac{ 180^\circ }{ \pi } \cdot \arccos((-132)/(24.5967 \cdot \ 25.6125)) \doteq 102.0948 = 0 ^\circ$

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#### Following knowledge from mathematics are needed to solve this word math problem:

For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc. Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator. Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation. Pythagorean theorem is the base for the right triangle calculator.

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