Question

In Problems 49-54, find the unit vector in the same direction as $\mathbf{v}$. $\mathbf{v}=-3 \mathbf{j}$

   In Problems 49-54, find the unit vector in the same direction as $\mathbf{v}$.
 $\mathbf{v}=-3 \mathbf{j}$

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Michael Sullivan 4th Edition

Chapter 8, Problem 50

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In this problem, $\mathbf{v} = -3 \mathbf{j}$. This vector points in the negative direction along the y-axis. Show more…

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In Problems 49-54, find the unit vector in the same direction as $\mathbf{v}$. $\mathbf{v}=-3 \mathbf{j}$

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Key Concepts

Normalization

Normalization is the process of scaling a vector so that its magnitude becomes one, while retaining its direction. This is achieved by dividing each component of the vector by its magnitude, resulting in a unit vector that represents the same direction as the original vector.

Unit Vector

A unit vector is a vector that has a magnitude of one and is used to indicate only the direction of the original vector. Converting any given vector into a unit vector, known as normalization, is useful in applications such as defining coordinate directions or when only the orientation of the vector is required.

Vector

A vector is a mathematical entity characterized by both magnitude (length) and direction. Vectors are represented by arrows in space, where the arrow's length indicates the magnitude and the arrow's orientation indicates the direction, making them essential for describing quantities in physics and engineering.

Magnitude

The magnitude of a vector is its length and is computed as the square root of the sum of the squares of its components. This scalar value measures how large the vector is, irrespective of its direction, and is crucial when normalizing a vector or comparing different vectors.

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