Finding the slope of the tangent line. Recall that the slope of the tangent line for a point in
The slope of the tangent line at this point is
Finding a unit vector parallel to the tangent line. Since slope is the ratio of rise per run or
Finding another unit vector. However, this is not the only answer! This points toward the first quadrant since both components are positive. Another possible answer is the vector antiparallel to this (parallel but pointing in the opposite direction, the third quadrant in this case). Hence, we negate both components to get another answer:
To find parrallel unit vectors to the line tangent ot point
Equation of a parrellel line. Point satisfying equation.
magnitude of the vector along our parrallel line, with end at the point
normalizing components of the vector at our chosen point, to find the unit vector. The positve and negative of this vector are parrallel.