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Given:- ;
, 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,
Therefore, we have ,
take t common in above equation we get,
⇒ or
To find the solution for t;
take
The number 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>
Multiply each term in the parentheses, namely 2/3 and 3x, by the only term outside of the parentheses, -4.
Each of the resulting products becomes a new term in the addition.
You may choose to keep the answer this way, or continue to change the improper fraction into a proper fraction. A lot of teachers also prefer to have the highest degree terms (terms that have variables with the highest powers) on the left.