If the line lies in the plane, lx + my – z = 9, then l^2 + m^2 is equal to

• 3D Geometry

If the line, (x-3)/2 = (y+2)/-1 = (z+4)/3, lies in the plane, lx + my – z = 9, then l² + m² is equal to:

1. 18
2. 5
3. 2
4. 26

Solution

As line lies on the plane, the line is perpendicular to the normal of the plane.

2l – m – 3 = 0 ... [Equation 1]

Also, point (3, –2, –4) lies in the plane.

3l – 2m + 4 = 9

3l – 2m – 5 = 0 ... [Equation 2]

From equation (1) and (2), you get

l = 1 and m = –1

So l² + m² = 2

The correct option is C.