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##