Final answer:
The set of parametric equations for the line tangent to → r ( t ) at point ( -19 , 12 , -11.513 ) can be found by differentiating the vector function → r ( t ) and substituting the coordinates of the given point.
Step-by-step explanation:
The set of parametric equations for the line tangent to → r ( t ) at point ( -19 , 12 , -11.513 ) can be found using the derivative of the vector function → r ( t ). Let's assume the vector function → r ( t ) is given by → r ( t ) = f( t ) i + g( t ) j + h( t ) k. To find the derivative, differentiate each component of the vector function with respect to t: → r'( t ) = f'( t ) i + g'( t ) j + h'( t ) k.
Now, let's substitute the x, y, and z coordinates of the given point into the equations for f( t ), g( t ), and h( t ) respectively. This will give us the specific values of f( t ), g( t ), and h( t ) at the given point. These values will represent the direction of the tangent line. Therefore, the set of parametric equations for the line tangent to → r ( t ) at the given point is:
x( t ) = f( t ),
y( t ) = g( t ),
z( t ) = h( t ).