Question

Find an equation for the plane that is perpendicular to v = (1, 1, 1) and passes through (1, 0, 0).

Answer 1

The equation for the plane that is perpendicular to the vector v = (1, 1, 1) and passes through the point (1, 0, 0) is x + y + z = 1.

Step-by-step explanation:

To find an equation for the plane that is perpendicular to the vector v = (1, 1, 1) and passes through the point (1, 0, 0), we need to use the normal vector v as the coefficient of the variables in the plane equation.

Step 1: The vector v is perpendicular to the plane, so its components are the coefficients of x, y, and z in the plane equation. Since v has components (1, 1, 1), the plane equation can be written as x - y - z = D, where D is a constant.

Step 2: The plane passes through the point (1, 0, 0). Substituting these coordinates into the plane equation allows us to find D.

Substituting, we get 1(1) + 1(0) + 1(0) = D. Hence, D = 1. Therefore, the equation of the plane is x + y + z = 1.

Answer 2

The perpendicular vector delivers you the coefficients of the x,y,z variables, so you know that your plane will have the equaction x+y+z = c.

Now all you have to do is find c to make the plane pass through (1,0,0).

If you fill in this point, you get c=1, so the equation is:

x+y+z=1.