Here are the essential concepts you must grasp in order to answer the question correctly.
Unit Vector
A unit vector is a vector that has a magnitude of one and indicates direction. To find a unit vector in the same direction as a given vector, you divide the vector by its magnitude. This process normalizes the vector, ensuring it retains its direction while having a length of one.
Recommended video:
Unit Vector in the Direction of a Given Vector
Magnitude of a Vector
The magnitude of a vector is a measure of its length and is calculated using the formula √(x² + y²) for a two-dimensional vector represented as (x, y). In the case of the vector v = i - j, the components are 1 and -1, leading to a magnitude of √(1² + (-1)²) = √2, which is essential for normalizing the vector.
Recommended video:
Finding Magnitude of a Vector
Direction of a Vector
The direction of a vector is determined by the angle it makes with a reference axis, typically the x-axis. For the vector v = i - j, the direction can be visualized in the Cartesian plane, where the vector points diagonally downwards. Understanding direction is crucial when finding a unit vector, as it ensures the resulting unit vector points in the same way as the original vector.
Recommended video:
Finding Direction of a Vector