This is the solution to the problem. However, I don't understand how they got to the part that says "and the parallel vector is $i+4j$..". What does this mean and how did they derive that?
Finding the unit vectors parallel to a tangent line
0
$\begingroup$
multivariable-calculus
1 Answers
2
For any real number $m$, the vector $(1,m)$ determines a line of slope $m$ through the origin: simply note that the line through $(0,0)$ and $(1,m)$ has rise $m$ and run $1$.
In this case, your $m=4$, so the vector $(1,4) = 1i + 4j = i+4j$ is a vector of the appropriate slope, hence parallel to the tangent.
-
0It depends on how you "know" the line. Lines through the origin in 3D need more than a single number to be determined (while in 2D the slope does it). If you know two points on the line, then the vector determined by their difference gives you a direction. – 2011-02-07