The 3rd pattern F Major scale takes it’s root note positions from the G shape open chord. When looking at the open G chord, the root notes are on the open G string and the 3rd fret Top and Bottom E strings.
G
Important: The notes used in the F Major scale are F, G, A, Bb, C, D, E, F, there is one flat in the F Major scale.
If we take a look at the scale on the fretboard, you will see something like the following pattern… the root notes are marked with the “X“
| | $3.9 | $1.10.$2.10.$3.X.$4.10.$5.10.$6.10 | $2.11 | $1.12.$3.12.$4.12.$5.12.$6.12 | $1.X.$2.13.$5.13.$6.X |
Note: In the diagram above it’s the fret numbers that are indicated not the scale degrees, and it isn’t the way you would normally write out a scale using TAB, it’s just to illustrate the fingering pattern of the scale. 
When playing this scale on the guitar, I normally start on the lowest pitch root note, the 13th fret Bottom E string with the pinky finger, and play up to the highest pitch note of the scale, 1st string 13th fret, which is also one of the scales F root notes.
| $6.13 $5.10 12 13 $4.10 12 $3.9 10 12 $2.10 11 13 $1.10 12 13 |
Descending back to the lowest pitch note of the scale, the C at the 8th fret bottom E string.
| $1.13 12 10 $2.13 11 10 $3.12 10 9 $4.12 10 $5.13 12 10 $6.13 12 10 |
Then back up in pitch to the F root note on the 13th fret bottom E string.
| $6.10 12 13 |