MHB Find Vector Perpendicular to Plane

AI Thread Summary
To find a vector perpendicular to the plane defined by points P (1, 2, 3), Q (2, 3, 1), and R (3, 1, 2), the vector product of vectors PQ and PR is used. The vectors are calculated as PQ = (1, 1, -2) and PR = (2, -1, -1). The cross product PQ × PR is computed using the determinant of a matrix formed by these vectors. This method effectively yields a vector that is orthogonal to the plane formed by the three points. Understanding the vector product is essential for solving this problem.
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).
 
Mathematics 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} $
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

I Two vectors and two perpendicular lines
Replies
20
Views
2K
MHB Parametric Eqs: Find Line & Plane, Find Triangle Area
Replies
4
Views
1K
MHB How to know if plane is perpendicular to another plane?
Replies
2
Views
2K
B Vector perpendicular to a plane defined by two vectors
Replies
5
Views
3K
B Geometrical meaning of magnitude of vector product
Replies
9
Views
2K
I Expressing any given point on plane with one unique number
Replies
4
Views
2K
Given a vector, how to compute orthogonal plane
Replies
4
Views
3K
I Vector equation perpendicular to two equations
Replies
10
Views
2K
MHB Finding lines through given point perpendicular and parallel to given line
Replies
1
Views
1K
MHB Find Dot Product Between Vector CD & Vector K
Replies
4
Views
4K

Hot Threads

Recent Insights

Back
Top