Question

Write the scalar equation of this plane. [x, y, z] = [5, 4, -7] +s[0, 1, 0] +t[0, 0, 1]

Answer 1

i know i have to find the direction vectors

Answer 2

I think [0 1 0] and [0 0 1] are orthogonal to the vector normal to the plane
if you from the cross product, you get [1 0 0]= N (the normal vector)

N dot [x y z] = constant is (almost) in the form of a scalar equation
(a x + b y +c z= d)

N dot with any point on the plane (5 4 -7 is a good choice) gives the constant:
N dot [5 4 7]= 5

so that is the equation:
[1 0 0] dot [x y z] =5
that simplifies to
x = 5
as the scalar form

Answer 3

Thank youuu !!!