Question

Consider the plane that contains points A(2,3,1), B(-11,1,2), C(-7,-3,-6).
a) Find two vectors that are parallel to the plane.
Ans: AC, BC or AB will be parallel to the plane.

b) Find two vectors that are perpendicular to the plane.
Ans: if i find the normal vector then i can use dot product and use arbitrary values to find the two vectors

c) Write a vector equation of the plane
Ans: I have two points AC, BC or AB and i have the normal, so i use them to write the vector equation.

d) Write the scalar equation of the plane.
Ans: the normal vectors are my coefficients for the(x,y,z) therefore if i substitute a point to find the constant 'd'

e) Write an equation of the line through the x- and y- intercepts of the plane
Ans: Find the x and y intercepts and those will be my points my z value being zero and using the normal as direction vector


Are the answers correct? I am a little confused, please correct if i am wrong somewhere.