Chapter 12.4, Problem 78E

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Chapter
Section

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem
1 views

# ProofProve that a N = ‖ v × a ‖ ‖ v ‖ .

To determine

To prove: The expression aN=v×av.

Explanation

Formula used:

v=vT(t)a=aTT(t)+aNN(t)

and

T(t)×T(t)=0T(t)×N(t)=1

Proof:

Use the formula for velocity and acceleration vectors, and get v×a as:

v×a={vT(t)}×{aTT(t)+aNN(t)}=vaT(T(t)×T(t))+v

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