Vector 𝐀 has x and y components of -8.70 cm and 15.0 cm, respectively; vector 𝐁 has x and y comp

step 1 Okay, in this problem we're given two vectors. Vector A, and I'll write it in bracket notation,

Vector 𝐀 has x and y components of -8.70 cm and 15.0 cm,...

Vector $\overrightarrow{\mathbf{A}}$ has $x$ and $y$ components of $-8.70 \mathrm{cm}$ and $15.0 \mathrm{cm},$ respectively; vector $\overrightarrow{\mathbf{B}}$ has $x$ and $y$ components of 13.2 $\mathrm{cm}$ and $-6.60 \mathrm{cm},$ respectively. If $\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}+3 \overrightarrow{\mathbf{C}}=0,$ what are the components of $\overrightarrow{\mathbf{C}}$?

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Key Concepts

Component-wise Equations

When equating two vector expressions, their corresponding components must be equal. This principle means that vector equations can be decomposed into separate algebraic equations for each axis, which can be solved independently to find unknown components.

Scalar Multiplication

Scalar multiplication involves multiplying every component of a vector by a constant, or scalar. This operation scales the vector’s magnitude without changing its direction (as long as the scalar is positive), and it is essential when adjusting vector quantities in equations.

Vector Components

Vectors are quantities that have both magnitude and direction, and they are often represented by their components along coordinate axes. This representation allows for a clear and manageable way to perform operations on vectors by working separately with each axis.

Vector Addition and Subtraction

Adding or subtracting vectors involves combining or subtracting their respective components. This makes it simple to find the resultant vector by performing the arithmetic operations independently along each coordinate axis.

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