 # 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 = < v1 , v2 >
The magnitude || v || of vector v is given by
|| v || = √(v1 2 + v2 2)
and the direction of vector v is angle θ in standard position such that
tan(θ) = v2 / v1 such that 0 ≤ θ < 2π.

## Use of the calculator to Calculate Magnitude and Direction

1 - Enter the components v1 and v2 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.

 v1 = 10 , v2 = -10 Decimal Places = 2 Magnitude: ||v|| = Direction: θ = �

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

1. Use the calculator to find the direction of the vectors u = < - 2 , 3 > and v = < - 4 , 6 >. Why are they equal?
2. Find the direction of the vectors u = < 2 , 5 > and v = < - 2 , - 5 >. Why is the difference between the two directions equal to 180�?
3. 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�