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## Homework Statement

A particle of mass m follows a path given by

**r**= (Xo + at^2)

**x**+ bt^3

**y**+ ct

**z**

where o, a, b and c are constants, t is the time.

**x, y , z**should have hats on them showing they are position vectors (unit vectors).

1. Find the angular momentum

**L**of the particle about the origin.

2. Find the force

**F**required to produce this motion and verify explicitly that d

**L**/dt =

**r**x

**F**

## Homework Equations

## The Attempt at a Solution

L = r x p

p = mv

to get v differentiate r w.r.t time to get v = 2at.

**x**+ (3bt^2)

**y**+ c

**z**

Subsitute into the equation:

L = ((Xo + at^2)x + bt^3y + ctz) x m(2at.

**x**+ (3bt^2)

**y**+ c

**z**)

Now to perform the cross product, im a bit unsure here. For the cross product i have this formula:

r x p =

**x**(ry.pz - rz.py) -

**y**(rx.pz - rz.px) +

**z**(rx.py - ry.px)

where the

**x,y,z**are unit vectors and the other x,y and z's are in subscript showing the particular component of each vector. So im a bit confused because do i just subsitute the constants from my equations of r and p or do i include their respective unit vecotrs associated with each component? But if i did that i would get for example

**x x y**=

**z**so would make quite a difference.

Any thought guys, thanks