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## Homework Statement

**T**(tangent),

**B**(binormal),

**N**(normal) are an orthogonal triad of unit vectors of a curve in R3.

Given:

- d
**T**/ds = k**N** - d
**N**/ds = -k**T**+ t**B** - d
**B**/ds = -t**N**

Find vector

**w**so that these equations may be written in the form:

d

**v**/ds =

**w**x

**v**, where

**v**=

**T**+

**N**+

**B**

## Homework Equations

Given above!

## The Attempt at a Solution

I tried splitting

**v**(

**T + N + B**) into its components, as well as

**w**, and putting them into a matrix to find the determinant (for the cross product).

The matrix consists of <i, j, k>, w = <w1, w2, w3>, and v = <(T1 + N1 + B1), (T2 + N2 + B2), (T3 + N3 + B3)>.

However, taking the determinant/cross product gives mismatching components (

*ie.*j and k components supposedly add up to an i component). I'm not too sure where to go from here :(

**Note:**This is for a Multivariate Calculus course!

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