Question

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

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

Algebra and Trigonometry

Algebra and Trigonometry

Michael Sullivan 10th Edition

Chapter 10, Problem 28

Instant Answer

Solved by Expert Ashley Hanson

06/17/2020

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So, the magnitude of $-4\mathbf{v}$ is the same as the magnitude of $4\mathbf{v}$. Show more…

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

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Key Concepts

Vector Magnitude

Vector magnitude, also known as the length or norm of a vector, quantifies the distance of a vector from the origin in a coordinate system. It is found using the formula that takes the square root of the sum of the squares of its components, and it represents the overall size of the vector regardless of its direction.

Scalar Multiplication

Scalar multiplication involves multiplying a vector by a real number (scalar), which scales the magnitude of the vector by the absolute value of the scalar. This operation can change the length of the vector while preserving or reversing its direction depending on whether the scalar is positive or negative.

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