Question

If $|\mathbf{v}|=4,$ what is $\| 3 \mathbf{v} | ?$

   If $|\mathbf{v}|=4,$ what is $\| 3 \mathbf{v} | ?$

Algebra and Trigonometry

Algebra and Trigonometry

Michael Sullivan 10th Edition

Chapter 10, Problem 27

Instant Answer

Solved by Expert Ashley Hanson

06/17/2020

Step 1

The magnitude of a scalar multiple of a vector is the absolute value of that scalar times the magnitude of the vector. Mathematically, this can be represented as: \[|k\mathbf{v}| = |k| |\mathbf{v}|\] Show more…

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If $|\mathbf{v}|=4,$ what is $\| 3 \mathbf{v} | ?$

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Key Concepts

Vector Norm

The vector norm is a function that assigns a non-negative length or size to vectors in a vector space. It quantifies the magnitude of a vector regardless of its direction, providing a way to measure distances and lengths in various mathematical and applied contexts.

Scalar Multiplication in Vector Norms

The scalar multiplication property of norms states that if a vector is multiplied by a scalar, the norm of the resulting vector is equal to the absolute value of the scalar multiplied by the norm of the original vector. This property reflects how scaling a vector by a number affects its magnitude, making it a fundamental concept in linear algebra and analysis.

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