if l1,m1,n1 and l2,m2,n2 are the d.c.'s of two mutually perpendicular lines,show that the d.c.'s of the line perpendicular to both of these are m1n2-m2n1,nil2-n2l1,l1m2-l2m1

It is a simple formula. You can expand it and show that LHS = RHS. 

 

Or else, you can simply expand the denominator in the equation 4 and regroup the terms and you should reach what is written on the LHS here.