Question

In Problems 49-54, find the unit vector in the same direction as $\mathbf{v}$. $\mathbf{v}=3 \mathbf{i}-4 \mathbf{j}$

   In Problems 49-54, find the unit vector in the same direction as $\mathbf{v}$.
 $\mathbf{v}=3 \mathbf{i}-4 \mathbf{j}$

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 51

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In this case, $\mathbf{v} = 3\mathbf{i} - 4\mathbf{j}$. Show more…

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In Problems 49-54, find the unit vector in the same direction as $\mathbf{v}$. $\mathbf{v}=3 \mathbf{i}-4 \mathbf{j}$

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Key Concepts

Vector

A vector is an entity characterized by both magnitude (length) and direction. It is usually represented in a coordinate system using components along standardized directions, such as the basis vectors, which simplifies operations like addition and scalar multiplication.

Magnitude of a Vector

The magnitude (or norm) of a vector provides a measure of its length. It is calculated as the square root of the sum of the squares of its individual components, which is a fundamental concept in determining the size of the vector.

Unit Vector

A unit vector is a vector with a magnitude of one that indicates only the direction of the original vector. It is useful in expressing the direction of a vector without regard to how long the vector is.

Normalization

Normalization is the process of converting a vector into a unit vector. This is achieved by dividing each component of the vector by its magnitude, thus retaining the original direction while ensuring the resulting vector has a magnitude of one.

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