Final answer:
To find the equation of a plane parallel to two vectors that passes through a point, calculate the normal vector using the cross product of the given vectors and use the point to derive the plane's equation.
Step-by-step explanation:
To find the equation of a plane that is parallel to two given vectors and passes through a specific point, we first need to determine the normal vector to the plane. The normal vector is perpendicular to any vector that lies on the plane. Since we are given two vectors that the plane is parallel to, the normal vector can be found by taking the cross product of these two vectors.
Step 1: Identify the two given vectors, let's call them ℓ and ℔. Find the cross product ℓ × ℔, which will give us the normal vector ℓ℔.
Step 2: Use the point that the plane passes through, let's call it P(x0, y0, z0), to determine the equation of the plane. The equation of a plane with normal vector (A, B, C) that passes through the point P(x0, y0, z0) is given by: A(x-x0) + B(y-y0) + C(z-z0) = 0.
Insert the components of the normal vector and the coordinates of the point P into this equation to obtain the equation of the plane.