Equations of a plane and normals

Question

Q1a) Find the scalars a,b,c and k so that

ax + by + cz = k

is the equation of the plane containing P(-2,1,5), with normal n = (1,-4,1)

 

b) Which of the following points lie in this plane?

(4,2,4)

(-1,3,-1)

(-1,-1,-4)

 

c) Find the equation of the plane containing the point Q(1,-4,1) and perpendicular to the direction (5,1,-2)

Answer 1

1a)

Find the scalars a,b,c and k :

Answer 2

(b).

The points are (4, 2, 4), (-1, 3, -1) and (-1, -1, -4).

Answer 3

(c).

Point : Q = (1, -4, 1) and direction vector (5, 1, -2).