Two vectors are given by 𝐀=4.0 𝐱̂-2.0 𝐲̂ and 𝐁=1.0 𝐱̂+5.0 𝐲̂ . What is ( a) 𝐀+𝐁,(𝐛) 𝐁-𝐀, and (c)

Step 1:u000AFirst, we need to find the sum of vectors $u005Coverrightarrow{u005Cmathbf{A}}$ and $u005Coverrighta

Two vectors are given by 𝐀=4.0 𝐱̂-2.0 𝐲̂ and 𝐁=1.0 𝐱̂+5.0 𝐲̂...

Two vectors are given by $\overrightarrow{\mathbf{A}}=4.0 \hat{\mathbf{x}}-2.0 \hat{\mathbf{y}}$ and $\overrightarrow{\mathbf{B}}=1.0 \hat{\mathbf{x}}+5.0 \hat{\mathbf{y}} .$ What is $($ a) $\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}},(\mathbf{b}) \overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{A}},$ and (c) a vector $\overrightarrow{\mathbf{C}}$ such that $\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}}=0$ ?

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Key Concepts

Equilibrium in Vectors

Equilibrium in vectors refers to the condition where the sum of multiple vectors is zero, indicating a balanced system. This concept is important in physics and engineering, especially when analyzing forces acting on a body, as it allows one to determine a missing or balancing vector that, when added to the others, results in no net force or movement.

Vector Subtraction

Vector subtraction is closely related to vector addition and involves finding the difference between two vectors by subtracting their corresponding components. This operation can also be understood as adding a vector to the negative of another vector, which is useful for determining relative displacement or the difference in magnitude and direction between two vectors.

Vector Addition

Vector addition is a fundamental operation in vector algebra where two or more vectors are combined by adding their corresponding components. This operation is used to determine the net effect of multiple vectors acting together, such as combining forces or displacements, by summing the x-components together, the y-components together, and so on.

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