R3 Tangent Line at a Point (1,1,1) for x=t^4, y=t^4, z=t^3

In summary, the conversation is about finding parametric equations for the tangent line to a curve and determining the value of t to plug in. The solution is to set x, y, and z equal to 1, which would make t=1.
  • #1
cybercrypt13
87
0

Homework Statement



Find parametric equations for the tangent line to the curve x= t^4, y= t^4, z=t^3 at the point (1,1,1)

Homework Equations





The Attempt at a Solution



I understand everything about solving this problem with the exception of how to find what t =? to plug in. ie: This equation it equals 1, other problems I see it equals 0 or 2Pi, yet not a single place in 3 books do I see any mention as to how to determine what t is.

What magic are they doing to figure this out?

Thanks,
 
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  • #2
Why don't you understand why t=1 in this problem? Now you are confusing me.
 
  • #3
x= t^4= 1, y= t^4= 1, and z= t^3= 1. Is there one value of t that satisfies those equations?
 

FAQ: R3 Tangent Line at a Point (1,1,1) for x=t^4, y=t^4, z=t^3

What is the R3 Tangent line question?

The R3 Tangent line question is a mathematical problem that involves finding the equation of a tangent line to a curve in three-dimensional space. It is a common question in multivariable calculus and is used to test understanding of derivatives, vectors, and equations of lines.

How do you solve the R3 Tangent line question?

To solve the R3 Tangent line question, you first need to find the derivative of the given curve with respect to each variable. Then, you can use the derivative to find the slope of the tangent line. Next, you need to find a point on the curve that lies on the tangent line. Finally, you can use the point and slope to write the equation of the tangent line in point-slope form.

What is the significance of the R3 Tangent line question?

The R3 Tangent line question is significant because it helps us understand the relationship between curves and tangent lines in three-dimensional space. It also allows us to apply our knowledge of derivatives and equations of lines in a real-world context.

What are some tips for solving the R3 Tangent line question?

Some tips for solving the R3 Tangent line question include making sure you understand the concept of derivatives and how they relate to tangent lines, using visual aids such as graphs or diagrams to better understand the problem, and practicing with different types of curves and equations to improve your problem-solving skills.

Are there any common mistakes to avoid when solving the R3 Tangent line question?

Yes, some common mistakes to avoid when solving the R3 Tangent line question include forgetting to take the derivative, using the wrong point on the curve to find the slope of the tangent line, and making calculation errors. It is important to double-check your work and carefully follow the steps to ensure an accurate solution.

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