Question

In Problems 49-54, find the unit vector in the same direction as $\mathbf{v}$. $v=5 i$

   In Problems 49-54, find the unit vector in the same direction as $\mathbf{v}$.
$v=5 i$

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 49

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Here, $\mathbf{v} = 5\mathbf{i}$, which means it is a vector of magnitude 5 in the direction of the x-axis. Show more…

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In Problems 49-54, find the unit vector in the same direction as $\mathbf{v}$. $v=5 i$

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Key Concepts

Vector

A vector is a mathematical object characterized by both magnitude and direction. It is represented in a coordinate system using components, and is fundamental in describing quantities like force, velocity, and displacement.

Magnitude of a Vector

The magnitude or norm of a vector is a measure of its length or size, calculated typically by taking the square root of the sum of the squares of its components. This concept is essential for quantifying and comparing vectors.

Unit Vector

A unit vector is a vector with a magnitude of 1 that indicates direction only. It is derived from any given vector by dividing the vector by its magnitude, thus preserving its direction while standardizing its length.

Normalization

Normalization is the process of converting any vector into a unit vector by dividing it by its magnitude. This technique is widely used in various fields to simplify problems involving direction, ensuring that only the directional information is retained.

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