- #1
Ted123
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Homework Statement
[PLAIN]http://img576.imageshack.us/img576/1710/vectorp.png
Homework Equations
The Attempt at a Solution
I've done part (a) but how do I do (b)?
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Char. Limit said:Well, do you know how to find a tangent vector to the surface G?
Char. Limit said:This site may help you. Since your equation is defined in two variables u and v, I would try taking the partial derivatives with respect to u and v, and you should get two tangent vectors. Then you should check to see if they are linearly independent.
Char. Limit said:That's odd. I'm not sure you're doing it right, then... remember that:
1. [tex]\sqrt{cosh^2(u)} = cosh(u)[/tex]. This will simplify both of your calculations when finding the second unit tangent vector.
2. sin(pi/4) and cos(pi/4) are not zero.
Char. Limit said:What happened to the unit vectors i and j?
Char. Limit said:But that last line is just not true. -i+j does not equal 0.
Char. Limit said:Presumably, yes. And the link I provided above also shows you how to find the normal vector.
Vector calculus is a branch of mathematics that involves the study of vectors and their operations, such as addition, subtraction, and multiplication. It also includes the study of vector fields, which are functions that assign a vector to each point in a given space.
Solving part (a) and (b) in vector calculus homework allows you to practice and apply the concepts and techniques learned in class. It also helps you develop problem-solving skills and gain a deeper understanding of vector calculus.
The first step is to carefully read the instructions and understand the problem. Then, you should review the relevant concepts and equations, and use them to formulate a solution. It is also important to show your work and explain your reasoning to receive full credit.
Some common mistakes include using incorrect formulas or equations, not checking your work for accuracy, and not clearly explaining your steps and reasoning. It is also important to pay attention to units and make sure they are consistent throughout your solution.
Practice is key to improving your skills in vector calculus. Make sure to review and understand the concepts and techniques taught in class, and solve as many problems as you can. You can also seek help from your instructor or peers if you are struggling with a particular problem.