I recently read definition of a plane as "given an equation in 3-variables, the locus of the equation will be a plane if every point of the line joining any two points on the locus also lie on the locus". While the definition intuitively makes sense, my question is how do I mathematically solve the issue i.e. what if I have to find a equation which satisfies the given definition?

Alternatively I want to do this -:

I have to find a equation satisfying $X(x) + Y(y) + Z(z) = 0$ such that

$X(x1) + Y(y1) + Z(z1) = 0$ - (i)

$X(x2) + Y(y2) + Z(z2) = 0$ - (ii)

where (x1, y1, z1) and (x2, y2, z2) are two points on a line satisfying the equation and then

$X(x1 + kx2/1+k) + Y(y1 + ky2/1 + k) + Z(z1 + kz2/1 + k) = 0$ - (iii)

where k is an arbitrary constant.


Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.