Question

Write the equation of the plane with a normal vector n=⟨1,3,−4⟩ and the point (−1,−2, 3) lying on the plane. Eq: x+y+z=

Answer 1

The equation of the plane is x + 3y - 4z - 1 = 0.

Step-by-step explanation:

To write the equation of a plane, we need the normal vector (n) and a point on the plane. Given that the normal vector is n = ⟨1,3,−4⟩ and the point on the plane is (-1,-2,3), we can use the formula:

(x - x1)a + (y - y1)b + (z - z1)c = 0

Plugging in the values, we have:

(x - (-1))(1) + (y - (-2))(3) + (z - 3)(-4) = 0

Simplifying further, we get:

x + 3y - 4z - 1 = 0