If 𝐯=2, what is -4 𝐯 ?

Name: Problem 28, Chapter 8: Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Uploaded: 2020-06-17T12:54:44-08:00
Duration: 25 s
Channel: Ashley Hanson
Description: If 𝐯=2, what is -4 𝐯 ?

step 1 The magnitude of minus 4v is equal to the magnitude of minus 4 multiplied by the magnitude of v.

Question

If $\|\mathbf{v}\|=2$, what is $\|-4 \mathbf{v}\|$ ?

    If $\|\mathbf{v}\|=2$, what is $\|-4 \mathbf{v}\|$ ?

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Michael Sullivan 4th Edition

Chapter 8, Problem 28

Instant Answer

Solved by Expert Ashley Hanson

06/17/2020

Step 1

We know that the norm (or magnitude) of vector $\mathbf{v}$ is 2, i.e., $\|\mathbf{v}\| = 2$. We need to find the norm of the vector $-4 \mathbf{v}$. Show more…

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If $\|\mathbf{v}\|=2$, what is $\|-4 \mathbf{v}\|$ ?

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Key Concepts

Vector Norm

The vector norm is a measure that assigns a non-negative length or magnitude to a vector in a vector space. It is commonly used to determine the distance of a vector from the origin, and it plays an essential role in various fields of mathematics and physics.

Homogeneity of Norms (Scalar Multiplication)

This property states that when a vector is multiplied by a scalar, the norm of the new vector is the absolute value of the scalar multiplied by the norm of the original vector. Formally, for any scalar c and vector v, the property is expressed as ||c·v|| = |c|·||v||. This concept is crucial in understanding how scaling a vector affects its magnitude.

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