Binormal Vector: Direction at Point x

_N3WTON_ · Sep 15, 2014

Homework Statement

Suppose that you draw a point "x" in the middle of a page, and a curve going through "x" in such a way that the curve is going straight upward at the point "x" and is curving to the left. In what direction does the binormal vector "B" (at "x") point?

Homework Equations

None

The Attempt at a Solution

Hello, I am having some trouble really visualizing this problem. I know about the right-hand rule, but I am unsure how to apply it here (or whether or not it does even apply here). My thought on the problem was that since if the curve is going straight upward at "x" and curving left, then the binormal vector would point out of the page, no?

Char. Limit · Sep 16, 2014

This sounds correct. Since the point is going straight up, the tangent vector is straight up, which means the normal vector points to the right and the binormal vector points out of the page.

Binormal Vector: Direction at Point x

Homework Statement

Homework Equations

The Attempt at a Solution

FAQ: Binormal Vector: Direction at Point x

What is a binormal vector and what does it represent?

A binormal vector is a mathematical concept used in differential geometry to describe the direction of a curve in three-dimensional space. It represents the direction that is perpendicular to both the tangent vector and the normal vector at a specific point on the curve.

How is the binormal vector calculated?

The binormal vector is calculated by taking the cross product of the tangent vector and the normal vector at a given point on a curve. This results in a vector that is perpendicular to both of these vectors and represents the direction of the curve at that point.

What is the significance of the binormal vector in physics?

In physics, the binormal vector is used to describe the direction of motion of a particle moving along a curved path. It is also used in calculations involving torque and angular momentum.

Can the binormal vector change along a curve?

Yes, the binormal vector can change along a curve as the direction of the curve changes. This is because the tangent vector and normal vector also change, resulting in a new binormal vector at each point on the curve.

How is the binormal vector related to the Frenet-Serret formulas?

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