MHB Finding Points Parallel to a Plane

AI Thread Summary
The vector P = (1,2,-1) is parallel to the plane defined by the equation 7x + 2y + kz = 5, leading to the determination of the value of k. To find k, the normal vector of the plane, represented as <7, 2, k>, is used in the equation for points parallel to the plane. The calculation shows that substituting the point (1,2,-1) into the plane equation yields 11 - k = 5. Solving this equation results in k being equal to 6. The discussion emphasizes the relationship between a point and a plane's normal vector in determining parallelism.
Guest2
Messages
192
Reaction score
0
If the vector $P = (1,2,-1)$ is parallel to the plane $7x+2y+kz = 5$, then what's the value of $k$?
 
Mathematics news on Phys.org
Do you know how to find the general formula for points parallel to a plane?
 
Deveno said:
Do you know how to find the general formula for points parallel to a plane?

So we find another plane parallel to this in which the point $(1,2,-1)$ lies?

I think $\mathbf{n} \cdot (\mathbf{x-x_{0}}) = 0$ so

$<7,2,k><x-1,y-2,z+1> = 0 \\
\implies 7x+2y+kz+k = 11 \\

\therefore 11-k = 5 \\

\implies k = 6.$
 
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...
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...

Similar threads

Replies
3
Views
1K
Replies
1
Views
1K
Replies
7
Views
4K
Replies
6
Views
21K
Replies
3
Views
2K
Replies
8
Views
2K
Back
Top