How do i find the equation of a plane spanned by two vectors?

I have a plane spanned by 2 vectors:

A = (2,1,0)

B = (1,1,1)



I need to find the equation of the plane spanned by these two vectors attached at the point M = (-1,2,3)



I need the equation in the form Ax +By + Cz = D.How do i find the equation of a plane spanned by two vectors?The normal vector of the plane is orthogonal to any vector that lies in the plane. Take the cross product.



n = A X B = %26lt;2, 1, 0%26gt; X %26lt;1, 1, 1%26gt; = %26lt;1, -2, 1%26gt;



With the normal vector to the plane and a point in the plane we can write the equation of the plane. Remember, the normal vector is orthogonal to any vector that lies in the plane. And the dot product of orthogonal vectors is zero. Define R(x, y, z) to be an arbitrary point in the plane. Then vector MR lies in the plane.



n 鈥?MR = 0

n 鈥?%26lt;R - M%26gt; = 0

%26lt;1, -2, 1%26gt; 鈥?%26lt;x + 1, y - 2, z - 3%26gt; = 0

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

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

x - 2y + z + 2 = 0

x - 2y + z = -2How do i find the equation of a plane spanned by two vectors?3x+5y+2z=0