# Magnitude and Direction of a Vector - Calculator

An online calculator to calculate the magnitude and direction of a vector from it components.

Let v be a vector given in component form by

v = < v_{1} , v_{2} >

The magnitude || v || of vector v is given by

|| v || = √(v_{1}^{ 2} + v_{2}^{ 2})

and the direction of vector v is angle θ in standard position such that

tan(θ) = v_{2} / v_{1} such that 0 ≤ θ < 2π.

## Use of the calculator to Calculate Magnitude and Direction

1 - Enter the components v_{1} and v_{2} of vector v as real numbers and press "Calculate Magnitude and Direction". The outputs are the magnitude || v || and direction θ __in degrees__ of vector v.

## Use the calculator of Magnitude and Direction to Answer the Questions

- Use the calculator to find the direction of the vectors u = < - 2 , 3 > and v = < - 4 , 6 >. Why are they equal?
- Find the direction of the vectors u = < 2 , 5 > and v = < - 2 , - 5 >. Why is the difference between the two directions equal to 180°?
- Use the calculator to find the direction of the vectors u = < 2 , 1 > and v = < 1 , 2 >. Why is the sum of the two directions equal to 90°? Find other pairs of vectors whose directions add up to 90°