Find Vector Perpendicular to Plane

Click For Summary

Discussion Overview

The discussion revolves around finding a vector that is perpendicular to a plane defined by three points in three-dimensional space: P (1, 2, 3), Q (2, 3, 1), and R (3, 1, 2). The focus is on the mathematical approach to determine this perpendicular vector, specifically through the use of vector products.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant suggests using the vector product of two vectors derived from the points P, Q, and R to find a perpendicular vector.
  • Another participant expresses confusion regarding the concept of the vector product and its calculation.
  • Further clarification is attempted by providing the vectors $\vec{PQ}$ and $\vec{PR}$, along with the determinant setup for the vector product.

Areas of Agreement / Disagreement

There is no consensus on understanding the vector product, as some participants express confusion about the concept and its calculation.

Contextual Notes

Some participants may lack familiarity with vector operations, particularly the vector product, which could affect their understanding of the discussion.

brinlin
Messages
12
Reaction score
0
Find a vector that is perpendicular to the plane passing through the points P (1, 2, 3), Q (2, 3, 1), and R (3, 1, 2).
 
Physics news on Phys.org
vector product yields a vector perpendicular to two vectors ...

$\vec{PQ} \times \vec{PR}$
 
I'm sorry I don't really understand.
 
brinlin said:
I'm sorry I don't really understand.

you don't understand, or you don't know what a vector product is and how to calculate it?

$\vec{PQ} = (1,1,-2)$
$\vec{PR} = (2,-1,-1)$

$ \vec{PQ} \times \vec{PR} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 1& 1 & -2 \\ 2 &-1 &-1 \\ \end{vmatrix} $
 

Similar threads

MHB Finding the Equation of a Plane Perpendicular to a Given Line
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Orthogonal transformations preserve length
  • · Replies 1 ·
Replies
1
Views
2K
High School Vector perpendicular to a plane defined by two vectors
  • · Replies 5 ·
Replies
5
Views
3K
MHB Find Equation of Plane Perpendicular to Line $l(t)$
  • · Replies 1 ·
Replies
1
Views
2K
High School Geometrical meaning of magnitude of vector product
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Vector equation perpendicular to two equations
  • · Replies 10 ·
Replies
10
Views
2K
MHB Understanding Map Interpretation and Shadow Projection on a Plane
  • · Replies 19 ·
Replies
19
Views
2K
High School Understanding Bases of a Vector Space
  • · Replies 3 ·
Replies
3
Views
3K
MHB Find Dot Product Between Vector CD & Vector K
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad The vector to which a dual vector corresponds
  • · Replies 11 ·
Replies
11
Views
563