Question

Let $A, B, C, D, \ldots, Z$ be points in $\mathbb{R}^{3} .$ Simplify the given quantity. $\overrightarrow{A B}+\overrightarrow{B C}$

Name: Problem 3, Chapter 10: Calculus
Uploaded: 2022-02-13T07:18:10-08:00
Duration: 3 min 10 s
Channel: Shafiq Rehman
Description: Let A, B, C, D, …, Z be points in ℝ^3 . Simplify the given quantity. A B+B C

   Let $A, B, C, D, \ldots, Z$ be points in $\mathbb{R}^{3} .$ Simplify the given quantity.
$\overrightarrow{A B}+\overrightarrow{B C}$

Calculus

Laura Taalman, Peter… 1st Edition

Chapter 10, Problem 3

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Solved by Expert Shafiq Rehman

02/13/2022

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We have two vectors: $\overrightarrow{AB}$ and $\overrightarrow{BC}$. Show more…

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Let $A, B, C, D, \ldots, Z$ be points in $\mathbb{R}^{3} .$ Simplify the given quantity. $\overrightarrow{A B}+\overrightarrow{B C}$

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Key Concepts

Vector Addition

Vector addition is the process of combining two or more vectors to form a resultant vector. In Euclidean space, it involves adding corresponding components of the vectors, and it satisfies the commutative and associative properties. This operation is crucial in many fields, as it allows complex motions or forces to be broken down into simpler parts or combined for analysis.

Path Independence of Displacement Vectors

When adding displacement vectors that form a connected path, intermediate points cancel out, leading to a direct vector from the starting point to the ending point. This property, often called the telescoping sum, shows that the sum of consecutive displacements along a path equals the overall displacement, making the calculation of net effect straightforward.

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