# Unit tangent and unit normal vectors.

Not what you're looking for?

Given the vector r(t) = t i + t^2 j find T(t), T(1) a dn then N (1).

After this I am to sketch the plane curve and graph the vectors T(1) and N(1) at t = 1.

##### Purchase this Solution

##### Solution Summary

Unit tangent and unit normal vectors are investigated. The solution is detailed and well presented.

##### Solution Preview

Solution:

r(t) = t i + t^2 j

First we find the unit tangent vector

T(t) = (i+2tj)/ sqrt(1+4t^2)

Now use the quotient rule to find T '(t)

T'(t) = (1+4t^2)^1/2 (2j) - (i+2tj) 4t (1+4t^2)^ -1/2

______________________________________

...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Probability Quiz

Some questions on probability

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.