↗️ Vector Addition Explorer

Adjust the X and Y components of Vector u and Vector v. The visual shows the "Head-to-Tail" method to find the green Resultant Vector (w)!

Vector u
(3, 4)
Length: 5.00
Vector v
(4, -1)
Length: 4.12
Resultant w (u+v)
(7, 3)
Length: 7.62
u v w

Vector u Components

X Component
3
Y Component
4

Vector v Components

X Component
4
Y Component
-1

📝 The Math Breakdown

  • Component Addition: To find the Resultant vector (w), simply add the X components together and the Y components together.
    Formula: w = (ux + vx, uy + vy)
    Calculation: w = (3 + 4, 4 + -1) = (7, 3)
  • Resultant Magnitude: The length of the resultant vector is found using the Pythagorean Theorem on its new components.
    Formula: Length = √(wx² + wy²)
    Calculation: Length = √(7² + 3²) = √58 ≈ 7.62