To calculate the direction of the vector v = (x, y), use the formula θ = arctan(y/x). For vectors in quadrant 1, the direction is θ , in quadrant 2 the direction is 180° – θ , in quadrant 3 the direction is 180° + θ and in quadrant 4 the direction is 360° – θ .

The x and y components of a vector form a right triangle. You can use the tangent function to find the angle between the x-axis and the vector. This wikiHow guide will show you how to find the direction of a vector and walk through four examples. Additionally, we’ll review how to find the magnitude of a vector.

The magnitude of a vector v whose components are given by <x 1, y 1 > is given by the formula |v| =√(x 1 2 + y 1 2). A vector has a direction and a magnitude. The individual measures of the vector v along the x-axis, y-axis, and z-axis are encapsulated using this

Magnitude of a Vector. The magnitude of a vector is shown by two vertical bars on either side of the vector: |a| OR it can be written with double vertical bars (so as not to confuse it with absolute value): ||a|| We use Pythagoras' theorem to calculate it: |a| = √( x 2 + y 2)

One of the following formulas can be used to find the direction of a vector: tan θ = y x , where x is the horizontal change and y is the vertical change or