1. What if the scalar product of two vectors is zero?

If the scalar product of two vectors is zero this means that the two vectors are perpendicular or cross at right angles.

2. Can the scalar product be used for three dimensional vectors?

Yes, the methods used are the same as those used for two dimensional vectors.

3. Can the ratio theorem be used to find the mid-point of a line?

Yes, the values of  λ and μ simply become 1/2 and 1/2.