Can a scalar product of two vectors be zero even when neither of them is a zero vector?

Yes; the scalar product of two vectors will be zero if the two vectors are perpendicular to each other.
Here is a simple example:
If ##stackrel(rarr)(A) = (1,0) and stackrel(rarr)(B)=(0,1)##
then ##stackrel(rarr)(A)*stackrel(rarr)(B) = 1xx0+0xx1=0##
In general the scalar (dot) product of two vectors is given as:
##stackrel(rarr)(A)*stackrel(rarr)(B)= ||A|| ||B|| cos(theta)##
where ##theta## is the angle between ##stackrel(rarr)(A)## and ##stackrel(rarr)(B)##
So if ##stackrel(rarr)(A)## is perpendicular to ##stackrel(rarr)(B)##
then ##theta = pi/2## and ##cos(theta)=0##
##rArr stackrel(rarr)(A)*stackrel(rarr)(B) = 0##