Purchase Solution

Radius of Curvature

Not what you're looking for?

Ask Custom Question

(a) Find the point of intersection of the line containing the points (3; 2; 1) and (4; 3; 3), and the plane containing the points (5; 4; 2), (3; 1; 6) and (6; 5; 3).

(b) Find the radius of curvature at (1; 0; 1) on the three dimensional curve given by
r(t) = cos ti + sin tj + e^tk. Sketch this curve, and briefly describe its shape.

Purchase this Solution

Solution Summary

The equation of the line given in the parametric form is depicted.

Solution Preview

Dear Student,
Please see the attachment for complete solution.

Best wishes,
OTA

(i) As is known the equation of the line which contains the points ( ) and ( ) is

, (1)

Here we have = 3, = 2, = 1 , and 4, 3, 3. Hence, from (1) we obtain

, , .

Therefore, the equation of the line, given in the parametric form is

, . (2).

Let us now write the equation of the plane which contains points ( ), ( ) and . It is known that it has a form the determinant

=0, (3)

Here = 5, = 4, = 2, 3, 1, 6 and 6, =5, =3. Let us substitute these values in (3), and then evaluate the ...

Purchase this Solution


Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

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.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

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

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.