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# Lesson 11.3: Vectors

## Explanation

Vectors are often displayed as letters with arrows above them similar to rays. However, vectors may also be shown as boldfaced lower case letters and appear without an arrow. A double-barbed arrow or a single-barbed arrow may be displayed above the letters. The most common usage is a single-barbed arrow with the barb to the right and on top of the shaft. This might also be referred to as a half-barb. In general, a full-barbed arrow indicates a ray and a single-barbed arrow indicates a vector.

Sometimes a text may consistently display arrows above vectors that are also displayed in bold print. If arrows are consistently used above vectors that are also shown in boldface type throughout a text, the arrows must be omitted in braille unless the author specifically refers to the vectors with the arrows, as part of a notational explanation. The boldface font is enough of an indication that the symbol shown is a vector in both print and in braille. Therefore, a the vector displayed as a bold v with an arrow over it would normally be displayed simply as >.

### Example 1

(this requires implementation of the five step rule)

$\stackrel{⇀}{n}$
⠐⠝⠣⠒⠒⠈⠕⠻

### Example 2

the sign of operation follows the termination indicator of the first vector

$\stackrel{⇀}{n}+\stackrel{⇀}{u}$
⠐⠝⠣⠒⠒⠈⠕⠻⠬⠐⠥⠣⠒⠒⠈⠕⠻

### Example 3

with signs of grouping - vectors are considered single units

$\stackrel{⇀}{m}=\frac{2}{3}\left(\stackrel{⇀}{v}-\stackrel{⇀}{u}\right)$
⠐⠍⠣⠒⠒⠈⠕⠻⠀⠨⠅⠀⠹⠆⠌⠒⠼⠷⠐⠧⠣⠒⠒⠈⠕⠻⠤⠐⠥⠣⠒⠒⠈⠕⠻⠾

### Example 4

when used in the context of a sentence

$\text{Find the the magnitude of}\phantom{\rule{.3em}{0ex}}\stackrel{⇀}{a}\text{.}$
⠠⠋⠊⠝⠙⠀⠞⠓⠑⠀⠍⠁⠛⠝⠊⠞⠥⠙⠑⠀⠕⠋⠀⠸⠩⠀⠐⠁⠣⠒⠒⠈⠕⠻⠀⠸⠱⠲