Finding Normal & Tangent Vectors to Line: 3x-2y-4

In summary, the conversation discusses finding the normal and tangent vectors to a given line, specifically the line 3x-2y-4. The participants share their methods and concerns, with one mentioning using formulas and the other suggesting to think more about the problem. The correct equation for a line and a plane are also clarified.
  • #1
Lancelot59
646
1
I figured this would be easy, I need to find the normal and tangent vectors to this line:

3x-2y-4

Well simple enough, I got the correct parametric equations for the normal, but the tangent line is being silly. I dumbed it out and got the right answer, but I think it was for the wrong reason.

I just treated the coefficients as the slope for the other variable, and it worked. I know that won't work all the time though. As shown by the next problem I did where the function was

[tex]e^{x}sin(y)=2[/tex] at the point [tex](ln(2),\frac{\pi}{2})[/tex]. I got (2,0) for the gradient at the point, and then did the same thing.

I got the correct parametric functions, but the method seems flawed. What's the proper way to do this?
 
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  • #2
hi,

you should think more about what you're doing instead of relying on formulas so heavily.

finding the tangent line to a line will be pretty trivial.

As far as the normal vector is concerned, you shouldn't have to look too far to find a solution. There are a few ways, and I suggest searching google first.
 
  • #3
How is 3x-2y-4 a line?
 
  • #4
SammyS said:
How is 3x-2y-4 a line?
...?
 
  • #5
dacruick said:
...?
3x-2y-4 is not an equation!

3x-2y-4 = 0 is the equation of a line.

z = 3x-2y-4 is the equation of a plane.
 
  • #6
SammyS said:
3x-2y-4 is not an equation!

3x-2y-4 = 0 is the equation of a line.

z = 3x-2y-4 is the equation of a plane.

Haha right you are. I honestly assumed there was an "=0". I think my brain automatically put it there.
 
  • #7
dacruick said:
Haha right you are. I honestly assumed there was an "=0". I think my brain automatically put it there.

Mine did too when I made the post.
 

FAQ: Finding Normal & Tangent Vectors to Line: 3x-2y-4

1. What is a normal vector to a line?

A normal vector is a vector that is perpendicular to a line. In other words, it is a vector that forms a 90 degree angle with the line at a given point.

2. How do you find the normal vector to a line?

To find the normal vector to a line, you first need to determine the slope of the line. This can be done by rearranging the equation of the line into the slope-intercept form, y = mx + b. The normal vector will then have a slope that is the negative reciprocal of the line's slope. For example, if the line has a slope of 2, the normal vector will have a slope of -1/2.

3. What is a tangent vector to a line?

A tangent vector is a vector that is parallel to a line at a given point. It is a vector that "touches" the line at that point but does not intersect it.

4. How do you find the tangent vector to a line?

To find the tangent vector to a line, you can first find the slope of the line at a given point using the derivative of the line's equation. The tangent vector will then have the same slope as the line at that point. You can also find the tangent vector by taking the cross product of the normal vector and the line's direction vector at that point.

5. Why are normal and tangent vectors important in calculus?

Normal and tangent vectors are important in calculus because they allow us to understand the behavior of a curve or line at a given point. They help us determine the direction of the curve or line at that point and are used in many calculus concepts, such as finding the derivative, calculating rates of change, and determining the direction of motion of a particle on a curve. They also have applications in physics, engineering, and computer graphics.

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