Find a parametric equation for the line through the point ( - 5, - 6, - 6) and perpendicular to the plane 2x + 3y + 9z = 17 which is written using the coordinates of the given point and the coefficients of x, y, and z in the given equation of the plane. type expressions using t as the variable.)

x=-5+2t, y=-6+3t, z=-6+9t

Step-by-step explanation:

We need to find parametric equations for the line through the point ( - 5, - 6, - 6) and perpendicular to the plane 2x + 3y + 9z = 17 .

If a line passes through a point and perpendicular to the plane , then the Cartesian form of line is

and parametric equations are

For the given information, . So, the Cartesian form of line is

Parametric equations of the line are

Therefore the parametric equation for the line are x=-5+2t, y=-6+3t, z=-6+9t.