Question

How to find the magnitude and direction of a vector?

Answer 1

. \mathcal{ magnitude and the direction of vector}

If vector v is defined by its components as follows v = < a , b >, its magnitude || v || is given by

|| v || = √(a2 + b2)

and its direction defined as the angle θ in standard position of the terminal side through the origin and point with coordinates (a , b).

Angle θ is found by solving the trigonometric equation

tan(θ) = b / a, such that 0 ≤ θ < 2π.

If the magnitude and direction are known, then

a = || v || cos (θ)

b = || v || sin (θ)