What is the Differential Length Vector at a Given Point on a Straight Line?

In summary, the conversation is discussing an expression for the differential length vector dl at a specific point on a straight line with given equations and a projection on the x-axis. The solution involves taking the derivative and using unit vectors in each direction. The person asking for help does not fully understand the problem but understands the solution provided. They are asking for more clarification on the "projection dx on the x-axis" part.
  • #1
mknut389
9
0
I got an answer for this, but it just doesn't seem correct. Maybe someone could tell me what I am doing wrong, or that I am just over thinking the problem and I am right.

Homework Statement



Write an expression for the differential length vector dl at the point (1,2,8) on the straight line y=2x, z=4y, and having the projection dx on the x-axis


Homework Equations



dl=dxax+dyay+dzaz


The Attempt at a Solution



y=2x, z=4y, therefore z=8x
therefore

dxax+2dxay+8dxaz.

since there are no variables remaining after you take the derivative, dl is then
1ax+2ay+8az

Any help would be amazing, and please excuse me if I am just being a complete idiot.

Thanks
 
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  • #2
That seems ok to me. So dl=dx(ax+2*ay+8*az). ax, ay and az are the unit vectors in each direction, right?
 
  • #3
Yes, ax, ay, az are the direction unit vectors. Thanks
 
  • #4
... I haven't really understood the problem, but i do understand the solution.. can anyone explain more about this problem especially the "projection dx on the x-axis" part..

please help me... i badly needed the explanation..

thanks in advance...
 

What is the concept of differential length?

The concept of differential length is a mathematical concept used to describe infinitesimal changes in length. It is often used in calculus to measure the length of a curve or to find the slope of a curve at a specific point.

What is the formula for finding differential length?

The formula for finding differential length is dL = √(dx² + dy²), where dx and dy represent the infinitesimal changes in x and y coordinates, respectively. This formula is derived from Pythagoras' theorem.

How is differential length used in physics?

In physics, differential length is used to calculate the distance traveled by a particle in a given time interval. It is also used to calculate the displacement of an object in a curved path, as well as to calculate the velocity and acceleration of an object at a specific point.

What is the difference between arc length and differential length?

Arc length is the total length of a curve, while differential length is the infinitesimal change in length at a specific point on the curve. In other words, arc length is the sum of all the differential lengths along a curve.

How is differential length related to the derivative?

Differential length is related to the derivative in calculus, where the derivative is used to find the instantaneous rate of change of a function at a specific point. The derivative of a function at a point is equal to the differential length of the function at that point.

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