Determine a vector perpendicular to the plane

In summary, the conversation discusses a problem with two parts: determining a vector perpendicular to a given plane and finding the area of a triangle. The solution for part a involves finding the cross product of two vectors, while the solution for part b involves finding half the magnitude of the perpendicular vector. The solution for part c is not clear as the question is not fully explained.
  • #1
joemama69
399
0

Homework Statement


this problem has 2 parts

a- Determine a vector perpendicular to the plane containing the points 1,0,0 2,0,-1 1,4,3
b - determine the area of the triangle

Homework Equations





The Attempt at a Solution



a- i found the two vectors from the 1st point a = i - k, b = 4j + 3k
and i believe a X b would yield a perpindicular vector
a X b = 4i - 3j + 4k, is this correct


b - isn't the area of the triangle 1/2 the magnitude of the perpindicular vecor

.5(4^2 + 3^2 + 4^2)^1/2 = 3.201 is this correct

b - i don't really understand what the question is asking

c - center is (4,-1,-3)
r = (-1 + (8^2 + 2^2 + 6^2)/4)^1/2 = 5 is this correct
 
Physics news on Phys.org
  • #2


Your answers to a and b are correct. What is the question for c?
 

1. What is a vector?

A vector is a mathematical object that has both magnitude (size) and direction. It is represented by an arrow, where the length of the arrow represents the magnitude and the direction of the arrow represents the direction. Vectors are commonly used in physics and engineering to describe quantities such as force, velocity, and acceleration.

2. What does it mean for a vector to be perpendicular to a plane?

A vector is said to be perpendicular to a plane if it is at a right angle, or 90 degrees, to every vector in the plane. This means that the vector is neither parallel nor in the same direction as any vector in the plane.

3. How do you determine a vector perpendicular to a plane?

To determine a vector perpendicular to a plane, you need to find two non-parallel vectors in the plane and then use the cross product to find a vector that is perpendicular to both of them. This vector will also be perpendicular to the plane.

4. What is the cross product?

The cross product is a mathematical operation that takes two vectors and produces a new vector that is perpendicular to both of the original vectors. It is represented by the symbol "x" and is calculated using a specific formula.

5. Can there be more than one vector perpendicular to a plane?

Yes, there can be an infinite number of vectors that are perpendicular to a plane. This is because for any two non-parallel vectors in the plane, you can use the cross product to find a new vector that is perpendicular to both of them. Therefore, there are infinite combinations of non-parallel vectors that can be used to find perpendicular vectors to the plane.

Similar threads

  • General Math
Replies
3
Views
783
Replies
6
Views
3K
  • Precalculus Mathematics Homework Help
Replies
20
Views
637
  • Calculus and Beyond Homework Help
Replies
1
Views
623
  • Calculus and Beyond Homework Help
Replies
3
Views
3K
  • Calculus and Beyond Homework Help
Replies
11
Views
3K
  • Calculus and Beyond Homework Help
Replies
2
Views
2K
  • Calculus and Beyond Homework Help
Replies
19
Views
2K
  • Calculus and Beyond Homework Help
Replies
9
Views
2K
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
Back
Top