Given:-    ;
  ;  , where a is any positive real number.
 , where a is any positive real number.
Consider the helix parabolic equation :  
                                               
now, take the derivatives we get;
                                             
As, we know that two vectors are orthogonal if their dot product is zero.
Here,   are orthogonal i.e,
  are orthogonal i.e,   
Therefore, we have ,
                                   

                                               

take t common in above equation we get,

⇒ or
 or 
To find the solution for t;
take 
The number determined from the coefficients of the equation
 determined from the coefficients of the equation 
The determinant 

Since, for any positive value of a determinant is negative.
Therefore, there is no solution.
The only solution, we have t=0.
Hence, we have only one points on the parabola   i.e <1,0>
 i.e <1,0>