Substitute (0, 0, 0) and (1, 0, 0) into the plane equation

I'll assume you're referring to the equation of a plane in 3D space, which is typically given in the form:

ax + by + cz = d

To substitute the points (0, 0, 0) and (1, 0, 0) into this equation, we'll need to find the values of a, b, c, and d that satisfy the equation.

Let's start with the point (0, 0, 0):

a(0) + b(0) + c(0) = d

This simplifies to:

0 = d

So we know that d = 0 for any plane that passes through the origin.

Now let's move on to the point (1, 0, 0):

a(1) + b(0) + c(0) = 0

This simplifies to:

a = 0

So we know that any plane that passes through the origin and the point (1, 0, 0) must have a coefficient of 0 for x.

We still need to find values for b and c, though. To do this, we can substitute the point (0, 1, 0) into the equation (since this point is guaranteed to lie in the plane as well):

a(0) + b(1) + c(0) = 0

This simplifies to:

b = 0

So any plane that passes through the origin, (1, 0, 0), and (0, 1, 0) must have coefficients of 0 for both x and y.

Finally, we can substitute the point (0, 0, 1) into the equation to find c:

a(0) + b(0) + c(1) = 0

This simplifies to:

c = 0

So any plane that passes through the origin, (1, 0, 0), (0, 1, 0), and (0, 0, 1) must have coefficients of 0 for x, y, and z.

Putting this all together, we can say that the equation of the plane that passes through the points (0, 0, 0) and (1, 0, 0) is:

0x + 0y + 0z = 0

Or simply:

0 = 0

This is a somewhat degenerate case, since there are infinitely many planes that pass through these two points (since they lie on a line). However, any plane that passes through these two points and the origin will satisfy the equation above.