Find a scalar equation of the plane that contains the given point P=(-3,-3,1)and the given normal vector n = (-1,4,7)
To find a scalar equation of a plane, we can use the formula:
Ax + By + Cz + D = 0,
where A, B, C, and D are constants, and (x, y, z) are the coordinates of any point on the plane.
In this case, we know that the plane contains the point P(-3, -3, 1) and has a normal vector n = (-1, 4, 7).
1. Substitute the coordinates of the point P into the equation:
-1(-3) + 4(-3) + 7(1) + D = 0
Simplify the equation:
3 - 12 + 7 + D = 0
Combine like terms:
-2 + D = 0
2. Solve for D:
D = 2
3. Rewrite the equation in scalar form:
-x - 4y - 7z + 2 = 0
So, the scalar equation of the plane that contains the point P(-3, -3, 1) and has a normal vector n = (-1, 4, 7) is -x - 4y - 7z + 2 = 0.