Vector v has the given direction angle and magnitude. Find the horizontal and vertical components.
θ = 50°, |v| = 26

Key Concepts

Direction Angle

The direction angle, often denoted as θ, is the angle formed between the positive x-axis and the line representing the vector in a Cartesian coordinate system. It is measured in degrees or radians and is crucial for determining the orientation of the vector. In this case, θ = 50° indicates that the vector is positioned 50 degrees counterclockwise from the positive x-axis.

Magnitude of a Vector

The magnitude of a vector, represented as |v|, is a measure of its length or size. It is a scalar quantity and is always non-negative. In this problem, the magnitude is given as 26, which means the vector extends 26 units from the origin in the direction specified by the angle θ.

Horizontal and Vertical Components

The horizontal and vertical components of a vector are the projections of the vector along the x-axis and y-axis, respectively. They can be calculated using trigonometric functions: the horizontal component is found using |v| * cos(θ), and the vertical component using |v| * sin(θ). For the given vector, these components will provide the exact coordinates of the vector's endpoint in the Cartesian plane.