Ruby, 38 (46) characters

e=->n,k,r{k-=r;'\|'[r]*k+'|/'[r]*n-=k}

This function takes the direction as an integer (1 for right, 0 for left). A function that takes a string is 8 characters longer:

d=->n,k,r{n-=k;r<?r??\\*k+?|*n :?|*~-k+?/*-~n}

Usage examples:

puts e[10, 5, 1] # or d[10, 5, 'r']
||||//////
puts e[10, 5, 0] # or d[10, 5, 'l']
\\\\\|||||

Haskell, 70

f R i l=(i-1)#'|'++(l-i+1)#'/'
f L i l=i#'\\'++(l-i)#'|'
(#)=replicate

assuming there is a type Direction, which has constructors R and L.

J - 32 26 char

J can't handle more than two arguments without using a list, and it can't handle non-homogenous lists without boxing. So having the input as a list of three integers is ideal. The parameter order is the reverse of the standard one: 0 for left or 1 for right, then position, then total number of dominoes. The reason for this is because J will end up going through them right-to-left.

{`(('|/\'{~-@>:,:<:)1+i.)/

I will add a more in-depth explanation later, but here's the gist of what's happening: F`G/ applied to a list x,y,z will evaluate x F (y G z). y G z constructs both possible ways the dominoes could have toppled, and then F uses x to select which of the two to use.

   {`(('|/\'{~-@>:,:<:)1+i.)/ 1 3 10
||////////
   {`(('|/\'{~-@>:,:<:)1+i.)/ 0 3 10
\\\|||||||

At the expense of a few characters, we can make the order the standard order: just append @|. to the end of the function. Adapting this to work with a string argument for direction would be much more costly, however.

Golfscript (53)

My first ever Golfscript program. Took me way longer than it should have and can probably be done in a smarter, more concise way (I'm sure someone will prove that :) ):

:d;:j;:i,{:x j<d'l'=&'\\'{x i j)->d'r'=&'/''|'if}if}%

A sample input is 10 5 'r'.

Ungolfed:

:d;:j;:i      # save input in variables and discard from stack, except total length i
,             # create an array of numbers of length i
{             # start block for map call
  :x          # save current element (= index) in variable
  j<          # check whether we are left of the first knocked over domino
  d'l'=       # check whether the direction is to the left
  &           # AND both results
  '\\'        # if true, push a backslash (escaped)
  {           # if false, start a new block
    x i j)->  # check whether we are on the right of the knocked over domino
    d'r'=     # check whether the direction is to the right
    &         # AND both results
    '/'       # if true, push a slash
    '|'       # if false, push a non-knocked over domino
    if
  }
  if
}%            # close block and call map

Python2/3 - 54

That last added on rule was quite nice (the 0/1 instead of 'l'/'r'). Made mine actually smaller than the existing python solution. 0 is left, 1 is right

def f(a,b,c):d,e='\|/'[c:2+c];h=b-c;return d*h+e*(a-h)

# Usage:
print(f(10,5,1)) # => ||||//////
print(f(10,5,0)) # => \\\\\|||||

GolfScript, 28 23 characters

'\\'@*2$'|/'*$-1%1>+@/=

Arguments on top of stack, try online:

> 10 5 1
||||//////

> 10 5 0
\\\\\|||||

PowerShell, 59 57

filter d($n,$k,$d){'\'*$k*!$d+'|'*($n-$k-$d)+'/'*++$k*$d}

Probably the same idea as every one else had.

• Takes either 0 or 1 as the direction parameter (for left and right, respectively)

JS (ES6) - 79 74 72 65

The 3rd param is a boolean (0: left / 1: right)

d=(a,b,c)=>"\\"[r="repeat"](!c&&a-b+1)+"|"[r](--b)+"/"[r](c&&a-b)

// Test
d(10,3,1); // => "||////////"
d(10,3,0); // => "\\\\\\\\||"

or

d=(a,b,c,d=b--)=>"\\|"[c].repeat(c?b:a-b)+"|/"[c].repeat(c?a-b:b)

Python 2.7, 68 65 61 59 58 chars

Use d=1 for left and d=0 for right

f=lambda a,p,d:['|'*(p-1)+'/'*(a-p+1),'\\'*p+'|'*(a-p)][d]

Note: Thanks to @TheRare for further golfing it.

Python - 45 52

This requires 1 for right and 0 for left.

x=lambda n,k,d:'\\|'[d]*(k-d)+"|/"[d]*(n-k+d)

Here's a version that takes r and l correctly, at 58:

def x(n,k,d):d=d=='r';return'\\|'[d]*(k-d)+"|/"[d]*(n-k+d)

Some usage examples...

>>> print(x(10,3,0))
\\\|||||||
>>> print(x(10,3,1))
||////////
>>> print(x(10,5,1))
||||//////
>>> print(x(10,5,0))
\\\\\|||||
>>> print(x(10,3,0))
\\\|||||||

PowerShell (107 96)

function d($a,$b,$c){-join(1..$a|%{if($_-ge$b-and$c){'/'}elseif($_-le$b-and!$c){'\'}else{'|'}})}

If we're allowed to treat the third parameter as an integer (0=l,1=r), then I can shave a little off here.

Test input:

d 10 5 r
||||//////
d 10 5 l
\\\\\|||||

Update:

d 10 5 1
||||//////
d 10 5 0
\\\\\|||||

If anyone by chance wants an explanation I will gladly add one. And as always I'm open to suggestions.

Original:

function d($a,$b,$c){-join(1..$a|%{if($_-ge$b-and$c-eq'r'){'/'}elseif($_-le$b-and$c-eq'l'){'\'}else{'|'}})}

Perl, 67 Characters

sub l{($t,$p,$d)=@_;$p--if$d;($d?'|':'\\')x$p.($d?'/':'|')x($t-$p)}

Assign the first three params (total, position, direction as an integer [0 left, 1 right]). Extras go into the ether. Subtract 1 from the position if we're headed right so the domino in position X is flipped, too.

C++ 181

#define C(x) cin>>x;
#define P(x) cout<<x;
int n,k,i;char p;
int main(){C(n)C(k)C(p)
for(;i<n;i++){if(p=='r'&&i>=k-1)P('/')else if(p=='l'&&i<=k-1)P('\\')else P('|')}
return 0;}

VBScript 109

I wish there was a better to do if/then

function f(a,p,d)
 f=string(a-p,"|")
 if d="r"then
   f=f+string(p,"/")
 else
   f=string(p,"\")+f
 end if
end function

C - 62 64 ('l':left, 'r':right)

f(a,b,c){for(b=a-b;a--;)putchar(c&2?a<b?47:124:a>b-2?92:124);}

C - 58 (0:left,1:right)

f(a,b,c){for(b=a-b;a--;)putchar(124-(a<b-!c?c*77:!c*32));}

AWK, 76

{ORS="";for(i=1;i<$2;i++)print"|";for(i=$2;i<=$1;i++)print($3=="r"?"/":"\\")}

Usage:

echo 10 5 r | awk '{ORS="";for(i=1;i<$2;i++)print"|";for(i=$2;i<=$1;i++)print($3=="r"?"/":"\\")}'

Although I'm wondering if I can nest ternary operators to make this shorter (although I'm playing around in bash right now and it doesn't seem like you can).

C# 124 ('\':left, '/':right)

String d(int c,int p,char d) {String result=""; for (int i=0;i<c;i++) {if(i>=c-p) {result+=d; } else {result+='|'; } } return result; }

first answer hope it satisfies request.

PHP, 89 Characters

function o($a,$p,$d){for($i=0;$i<$a;$i++)echo$d==0?($i+1>$p)?'|':'\\':($i+1<$p?'|':'/');}

Just because I love PHP.

PHP - 81

echo substr_replace(str_repeat('|',$l),str_repeat($r?'\\':'/',$f),$r?0:$f*-1,$f);
// Or the long version:
echo substr_replace(
            str_repeat('|',$l), // string
            str_repeat($r?'\\':'/',$f), // replace
            $r?0:$f*-1, //start
            $f// length
        );

$r = go to Right? boolean
$l = total Lenght
$f = Fallen dominos

Example results:

$r = true;  $l = 10; $f = 4; -> \\\\||||||
$r = false; $l = 10; $f = 5; -> |||||/////
$r = false; $l = 10; $f = 2; -> ||||||||//