Category:Examples of Vector Sum
This category contains examples of Vector Sum.
Let $\mathbf u$ and $\mathbf v$ be vector quantities of the same physical property.
Component Definition
Let $\mathbf u$ and $\mathbf v$ be represented by their components considered to be embedded in a real $n$-space:
\(\ds \mathbf u\) | \(=\) | \(\ds \tuple {u_1, u_2, \ldots, u_n}\) | ||||||||||||
\(\ds \mathbf v\) | \(=\) | \(\ds \tuple {v_1, v_2, \ldots, v_n}\) |
Then the (vector) sum of $\mathbf u$ and $\mathbf v$ is defined as:
- $\mathbf u + \mathbf v := \tuple {u_1 + v_1, u_2 + v_2, \ldots, u_n + v_n}$
Note that the $+$ on the right hand side is conventional addition of numbers, while the $+$ on the left hand side takes on a different meaning.
The distinction is implied by which operands are involved.
Triangle Law
Let $\mathbf u$ and $\mathbf v$ be represented by arrows embedded in the plane such that:
- $\mathbf u$ is represented by $\vec {AB}$
- $\mathbf v$ is represented by $\vec {BC}$
that is, so that the initial point of $\mathbf v$ is identified with the terminal point of $\mathbf u$.
Then their (vector) sum $\mathbf u + \mathbf v$ is represented by the arrow $\vec {AC}$.
Pages in category "Examples of Vector Sum"
The following 2 pages are in this category, out of 2 total.