Loading…
Loading…
VecLab
The basic 2D vector operations, together.
A vector encodes both magnitude and direction — unlike a plain number, (3, 4) isn't just 'size 5' (its magnitude via Pythagoras), it also points a specific way, which is why vector addition combines both components separately.
The dot product measures how much two vectors point in the same direction — it's zero when they're perpendicular, positive when they broadly align, and negative when they point opposite ways, which is why it's central to physics work/force calculations.
What you entered
Vector sum (add component-wise)
(3+1, 4+2)= (4, 6)Dot product
3×1 + 4×2= 11Magnitude |v₁|
√(3² + 4²)= 5Magnitude |v₂|
√(1² + 2²)= 2.2361Angle between them
cos⁻¹(11 ÷ (5×2.2361))= 10.3048°Result
Dot product: 11
v₁ and v₂ are 10.3° apart, with a dot product of 11 — a positive dot product means they broadly point the same way, negative means broadly opposite, and zero means perpendicular.