Question

In Problems 45-50, find the unit vector in the same direction as $\mathbf{v}$. $\mathbf{v}=-6 \mathbf{i}+12 \mathbf{j}+4 \mathbf{k}$

   In Problems 45-50, find the unit vector in the same direction as $\mathbf{v}$.
$\mathbf{v}=-6 \mathbf{i}+12 \mathbf{j}+4 \mathbf{k}$

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 48

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The vector given is $\mathbf{v} = -6\mathbf{i} + 12\mathbf{j} + 4\mathbf{k}$. Show more…

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In Problems 45-50, find the unit vector in the same direction as $\mathbf{v}$. $\mathbf{v}=-6 \mathbf{i}+12 \mathbf{j}+4 \mathbf{k}$

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Key Concepts

Unit Vector

A unit vector is a vector with a magnitude of 1 that indicates a direction. It is crucial for representing and comparing directions without influencing calculations with its length.

Vector Magnitude

The magnitude of a vector is a measure of its length, calculated as the square root of the sum of the squares of its individual components. It is essential for understanding the size of the vector and is used in various operations, including normalization.

Normalization

Normalization is the process of converting a vector into a unit vector by dividing it by its magnitude. This procedure retains the vector’s direction while standardizing its length to one, making it useful for simplifying and comparing directional data.

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