Question

If $\mathbf{m}=(7,-8)$ and $\mathbf{n}=(6,-9)$, find the product of -7 and $\mathbf{m}-\mathbf{n}$.

   If $\mathbf{m}=(7,-8)$ and $\mathbf{n}=(6,-9)$, find the product of -7 and $\mathbf{m}-\mathbf{n}$.

CliffsStudySolver Trigonometry

CliffsStudySolver Trigonometry

David Alan Herzog 1st Edition

Chapter 5, Problem 22

Instant Answer

Solved by Expert James Kiss

01/24/2022

Step 1

Step 1: Find the difference between $\mathbf{m}$ and $\mathbf{n}$: $\mathbf{m}-\mathbf{n} = (7,-8) - (6,-9) = (7-6, -8-(-9)) = (1,1)$. Show more…

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If $\mathbf{m}=(7,-8)$ and $\mathbf{n}=(6,-9)$, find the product of -7 and $\mathbf{m}-\mathbf{n}$.

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Key Concepts

Scalar Multiplication

Scalar multiplication is the operation of multiplying a vector by a scalar, a real number, which entails multiplying each component of the vector by that number. This operation scales the vector without changing its direction (unless the scalar is negative, which reverses the direction), and is critical for adjusting the magnitude of vectors in various mathematical and applied contexts.

Vector Subtraction

Vector subtraction involves subtracting the corresponding components of two vectors to form a new vector. This operation is performed component-wise, meaning that for vectors represented as (a, b) and (c, d), their difference is (a - c, b - d). It is a fundamental operation in vector arithmetic, used to determine the relative position or difference between two vectors.

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