Question

In Problems 49-54, find the unit vector in the same direction as $\mathbf{v}$. $\mathbf{v}=-5 \mathbf{i}+12 \mathbf{j}$

   In Problems 49-54, find the unit vector in the same direction as $\mathbf{v}$.
 $\mathbf{v}=-5 \mathbf{i}+12 \mathbf{j}$

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 52

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The vector given is $\mathbf{v} = -5\mathbf{i} + 12\mathbf{j}$. Show more…

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In Problems 49-54, find the unit vector in the same direction as $\mathbf{v}$. $\mathbf{v}=-5 \mathbf{i}+12 \mathbf{j}$

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Key Concepts

Unit Vector

A unit vector is a vector with a magnitude of 1 that indicates direction. It is often used to represent the direction of another vector without regard to its length, serving as a basis for expressing direction for computations in various applications.

Vector Magnitude

The magnitude of a vector is the length or size of the vector. It is computed using the square root of the sum of the squares of its components. This measure helps in comparing vectors and plays a crucial role in normalization.

Normalization

Normalization is the process of converting a given vector to a unit vector by dividing it by its magnitude. This operation retains the direction of the original vector while scaling its length to one, making it useful in many problems involving direction and scaling.

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