Direction of the Vector Calculator

What is the Direction of a Vector?

As the name implies, a vector indicates the direction of two different points when they are directed from one location to another. It can also be thought of as variations in velocity and speed. A vector’s orientation, or the angle it forms with the x-axis, determines its direction. For example, a line with an arrow on top and a fixed point at the other end represents a vector. We can determine the vector’s direction by looking at the tip of its arrowhead.

The direction of a Vector Formula

A line’s slope and a vector formula’s direction are connected. We are aware that \( \dfrac{y}{x} \) is the slope of a line through the origin and the coordinates (x, y). We also understand that this line’s slope, tan, equals \( \dfrac{y}{x} \) if θ is the angle it makes. Thus, the direction of a vector formula is:

\( θ = tan^{-1}(\dfrac{y}{x}) \)

where y is the vertical displacement, x is the horizontal displacement, and θ is the vector’s direction.

The direction for a vector line with starting point (\(x_1, y_1\)) and final point (\(x_2, y_2\)) is:

\( θ = tan^{-1} (\dfrac{y_2 – y_1}{x_2 – x_1}) \)

Example

Example 1: Determine the vector’s direction given that the vertical and horizontal displacements are 6 and 5, respectively.

\( y = 6 \) and \( x = 5 \)

Using the formula, we get,

\( θ = tan^{-1}(\frac{y}{x}) = tan^{-1} (\frac{6}{5}) = 50.19° \)

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