Direction of the Vector Calculator

The Mathematics Master direction of the vector calculator allows you to find the magnitude and direction of the vector from its individual components. The angle determines the direction of the vector it makes with the X-axis, also known as the horizontal axis.

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 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,

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


How to find a unit vector in the direction of the given vector?

We divide a vector by its magnitude to find a unit vector with the same direction. For example, consider a vector with a magnitude of |v|, such as v = (1, 4). Then, the unit vector uv, which is also in the same direction as v, is obtained by dividing each element of the vector v by the value of |v|.

What Is The Direction Of A Vector?

A physical quantity known as a vector has a magnitude and a direction. A vector diagram represents a vector quantity, and as a result, it has a direction. The direction of a vector is defined as the angle at which the vector points.

Can't find your query?

Fill out the form below with your query and we will get back to you in 24 hours.