Question

In Problems 33-38, find $\|\mathbf{v}\|$. $\mathbf{v}=6 \mathbf{i}+2 \mathbf{j}-2 \mathbf{k}$

   In Problems 33-38, find $\|\mathbf{v}\|$.
$\mathbf{v}=6 \mathbf{i}+2 \mathbf{j}-2 \mathbf{k}$

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 38

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Step 1

Given \(\mathbf{v} = 6\mathbf{i} + 2\mathbf{j} - 2\mathbf{k}\), the components of \(\mathbf{v}\) are \(6\) in the \(\mathbf{i}\) direction, \(2\) in the \(\mathbf{j}\) direction, and \(-2\) in the \(\mathbf{k}\) direction. Show more…

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In Problems 33-38, find $\|\mathbf{v}\|$. $\mathbf{v}=6 \mathbf{i}+2 \mathbf{j}-2 \mathbf{k}$

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Key Concepts

Euclidean Space

Vectors are often considered within Euclidean space, where each component represents a projection along an axis. In this setting, the norm calculation determines the distance from the origin to the point defined by the vector, following the familiar geometric interpretation of distance.

Vector Norm

The vector norm (or magnitude) is a measure of the length of a vector in a given space. It is computed by taking the square root of the sum of the squares of its components, which generalizes the Pythagorean theorem to higher dimensions.

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