Vector sum

The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?

Result

x =  17.35

Solution:

$|u+v|^2 = |u|^2+|v|^2-2|u||v|\cos (180 ^\circ -61 ^\circ ) \ \\ |u+v| = 17.35$

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Tips to related online calculators
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.
Cosine rule uses trigonometric SAS triangle calculator.

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