- #1
In summary, The conversation is about a student struggling with finding the right answer to a problem. They share their attempt at solving it and ask for help in finding where they went wrong. The expert summarizer points out that the cross-product was calculated incorrectly.
- #2
mfb
Mentor
- 37,145
- 13,988
Can you explain what you calculated there?
- #3
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
- 11,894
- 1,486
You calculated the cross-product incorrectly.uzman1243 said:Homework Statement
[IMG ]https://www.physicsforums.com/attachment.php?attachmentid=68806&stc=1&d=1397897233[/PLAIN]
Homework Equations
N/A
The Attempt at a Solution
The problem is that I don't get the right answer which is:
2x + y + 7z = -3.
Can you please help me find where I went wrong?
##\left( -2 + 0 \right)\hat i \ne 0\hat i ##
##\hat k \left( \ (1) (-3) - (-2)(-2)\ \right)\ne \hat k \left(-3 + 4 \right)##
Related to Finding equation of a plane with 3 points
1. How do you find the equation of a plane with 3 points?
To find the equation of a plane with 3 points, you can use the point-normal form of a plane equation, which is (x-a)(n) = 0, where x is a point on the plane, a is a known point on the plane, and n is the normal vector of the plane. Alternatively, you can use the cross product of two vectors formed by the given points to find the normal vector, and then use the point-normal form to find the equation.
2. Can I use any 3 points to find the equation of a plane?
No, you cannot use any 3 points to find the equation of a plane. The points must be non-collinear, meaning they cannot all lie on the same line. If the points are collinear, the plane is undefined and has no equation.
3. What is the significance of finding the equation of a plane with 3 points?
Finding the equation of a plane with 3 points allows you to represent the plane in a mathematical form, which can be useful in solving various problems in geometry and physics. It also helps in visualizing and understanding the orientation and position of the plane in relation to the given points.
4. Is there a difference in finding the equation of a plane in 2D vs 3D?
Yes, there is a difference in finding the equation of a plane in 2D vs 3D. In 2D, the equation of a plane is simply y = mx + b, where m is the slope and b is the y-intercept. In 3D, the equation of a plane is more complex and involves the use of vectors and cross products.
5. Can I use the equation of a plane to find the distance between a point and the plane?
Yes, you can use the equation of a plane to find the distance between a point and the plane. You can use the formula for the distance from a point to a plane, which is given by d = |(ax + by + cz + d)|/√(a² + b² + c²), where (x, y, z) is the given point and ax + by + cz + d is the equation of the plane in standard form.
Similar threads
-
Precalculus Mathematics Homework Help
-
Precalculus Mathematics Homework Help
-
Precalculus Mathematics Homework Help
-
Precalculus Mathematics Homework Help
-
Precalculus Mathematics Homework Help
-
Precalculus Mathematics Homework Help
-
Precalculus Mathematics Homework Help
-
Precalculus Mathematics Homework Help
-
Precalculus Mathematics Homework Help
-
Precalculus Mathematics Homework Help