Does the following point lie on plane?

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To determine if the point (8, 4, -5) lies on the plane defined by the equation 7x - 3y + 4z = 8, the values are substituted into the equation. The calculation shows that 7(8) - 3(4) + 4(-5) results in 24, which does not equal 8. Therefore, the point does not lie on the plane. The discussion also touches on the general understanding of the equation of a plane in the form Ax + By + Cz = D. The conclusion is that the point (8, 4, -5) is not on the specified plane.
salistoun
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Hi all,

I got this question from a past exam paper does the point (8 , 4 , -5) lie on the plane 7x - 3y + 4z = 8?

Do you work it out as follows because can't find this example in my Linear Algeria book?

7(8) - 3(4) + 4(-5) = 8
56 - 12 - 20 = 8
24 is not equal to 8
Therefore the following point does not lie on the plane.

Thanks
Stephen
 
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you can do that.
 
thanks Andrien
 
What do you understand the sentence "Ax+ By+ Cz= D is the equation of plane p" to mean?
 
I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...

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