DAT 300 Exam 1 Prep Questions with
complete solution 2025/2026
What is a scalar field? - correct answer ✔A function of several variables whose output is a single real
number (e.g. temperature).
What is a vector field? - correct answer ✔A function of several variables whose output is a vector (e.g.
velocity field).
How do you recognize a function vs. a relation in R^3? - correct answer ✔A function must assign
exactly one zzz-value for each (x,y)(x,y)(x,y). If multiple zzz-values exist, it is not a function.
General form of a plane in R^3? - correct answer ✔Ax+By+Cz=D.
What vector is orthogonal to a plane Ax+By+Cz=D? - correct answer ✔The normal vector ⟨A,B,C⟩.
Equation of a plane through P(x0,y0,z0) with normal ⟨A,B,C⟩? - correct answer ✔A(x−x0)+B(y−y0)
+C(z−z0)=0.
How do you find a unit normal vector to a plane? - correct answer ✔Divide the normal vector by its
magnitude.
One linear equation in R^3 represents what? - correct answer ✔A plane
Two independent linear equations in R^3 represent what? - correct answer ✔A line
Equation with one variable missing (e.g. x^2+y^2=1) represents what? - correct answer ✔A cylinder
(extruded along the missing axis).
complete solution 2025/2026
What is a scalar field? - correct answer ✔A function of several variables whose output is a single real
number (e.g. temperature).
What is a vector field? - correct answer ✔A function of several variables whose output is a vector (e.g.
velocity field).
How do you recognize a function vs. a relation in R^3? - correct answer ✔A function must assign
exactly one zzz-value for each (x,y)(x,y)(x,y). If multiple zzz-values exist, it is not a function.
General form of a plane in R^3? - correct answer ✔Ax+By+Cz=D.
What vector is orthogonal to a plane Ax+By+Cz=D? - correct answer ✔The normal vector ⟨A,B,C⟩.
Equation of a plane through P(x0,y0,z0) with normal ⟨A,B,C⟩? - correct answer ✔A(x−x0)+B(y−y0)
+C(z−z0)=0.
How do you find a unit normal vector to a plane? - correct answer ✔Divide the normal vector by its
magnitude.
One linear equation in R^3 represents what? - correct answer ✔A plane
Two independent linear equations in R^3 represent what? - correct answer ✔A line
Equation with one variable missing (e.g. x^2+y^2=1) represents what? - correct answer ✔A cylinder
(extruded along the missing axis).
