MN 553 FINAL PURDUE GLOBAL UNIVERSITY
CERTIFICATION PREPARATION 2026 REVIEW
SHEET SOLVED QUESTIONS GUARANTEED
PASS
◉ Sphere Formula
Answer: Standard Form: (x-h)²+(y-k)²+(z-l)²=r²
◉ How to solve a sphere not in standard form? (x²+y²+4x...)
Answer: Magic Number
◉ What is a vector?
Answer: A quantity with magnitude and direction.
◉ How to find the magnitude of a vector <a₁,a₂,a₃>
Answer: √(a₁²+a₂²+a₃²)
◉ Dot Product of 2 Vectors
Answer: a₁b₁+a₂b₂+a₃b₃
Scalar Value
,◉ Cross Product of 2 Vectors
Answer: This:
◉ What is the dot product of 2 vectors with an angle of 90° between
them?
Answer: 0
◉ What is the relationship between two vectors and the angle
between them?
Answer: a•b=|a||b|cos(theta)
◉ What is the relationship between a, b, and axb?
Answer: axb is perpendicular to both a and b
◉ How do you find the area of a parallelogram formed by two
vectors?
Answer: |axb|
◉ Equation of a line in 3D
Answer: r=<r₀>+t<v>
<line equation> = initial point + t*<slope vector>
,◉ Parametric form of the equation of a line
Answer: x=x₀+at
y=y₀+bt
z=z₀+ct
◉ Symmetric Form of the equation of a line
Answer: Start with parametric form
Solve each for t
Set them all equal to eachother
◉ SOLVE
Equation of a line through point <a,b,c> and parallel to vector <d,e,f>
Answer: r₀=given point
v=given vector
Plug in: r=<r₀>+t<v>
◉ SOLVE
Equation of a line segment from (a,b,c) to (d,e,f)
Answer: Use one of the points as r₀
Use <d-a,e-b,f-c> as v
Plug in: r=<r₀>+t<v>
MUST LIMIT RANGE OF T BECAUSE ITS A LINE SEGMENT
, ◉ Vector form of the equation of a plane
Answer: n•<x-x₀,y-y₀,z-z₀>=0
perpendicular vector • <x-point on plane and n, y-...>
◉ Scalar form of the equation of a plane
Answer: a(x-x₀)+b(y-y₀)+c(z-z₀)=0
x val of perpendicular vector (x-x point on plane and n) + ...
◉ SOLVE
Equation of plane through point (a,b,c) and perpendicular to
n=<d,e,f>
Answer: <d,e,f> • <x-a,y-b,z-c> = 0
d(x-a)+e(y-b)+f(z-c)=0
◉ SOLVE
Equation of plane containing points (a,b,c),(d,e,f),(g,h,i)
Answer: Use three points to get two vectors with the same base
point. u=<d-a,e-b,f-c> v=(g-a,h-b,i-c>
Find cross product. This is n.
Use the base point and n.
Plug in: n•<x-x₀,y-y₀,z-z₀>=0
CERTIFICATION PREPARATION 2026 REVIEW
SHEET SOLVED QUESTIONS GUARANTEED
PASS
◉ Sphere Formula
Answer: Standard Form: (x-h)²+(y-k)²+(z-l)²=r²
◉ How to solve a sphere not in standard form? (x²+y²+4x...)
Answer: Magic Number
◉ What is a vector?
Answer: A quantity with magnitude and direction.
◉ How to find the magnitude of a vector <a₁,a₂,a₃>
Answer: √(a₁²+a₂²+a₃²)
◉ Dot Product of 2 Vectors
Answer: a₁b₁+a₂b₂+a₃b₃
Scalar Value
,◉ Cross Product of 2 Vectors
Answer: This:
◉ What is the dot product of 2 vectors with an angle of 90° between
them?
Answer: 0
◉ What is the relationship between two vectors and the angle
between them?
Answer: a•b=|a||b|cos(theta)
◉ What is the relationship between a, b, and axb?
Answer: axb is perpendicular to both a and b
◉ How do you find the area of a parallelogram formed by two
vectors?
Answer: |axb|
◉ Equation of a line in 3D
Answer: r=<r₀>+t<v>
<line equation> = initial point + t*<slope vector>
,◉ Parametric form of the equation of a line
Answer: x=x₀+at
y=y₀+bt
z=z₀+ct
◉ Symmetric Form of the equation of a line
Answer: Start with parametric form
Solve each for t
Set them all equal to eachother
◉ SOLVE
Equation of a line through point <a,b,c> and parallel to vector <d,e,f>
Answer: r₀=given point
v=given vector
Plug in: r=<r₀>+t<v>
◉ SOLVE
Equation of a line segment from (a,b,c) to (d,e,f)
Answer: Use one of the points as r₀
Use <d-a,e-b,f-c> as v
Plug in: r=<r₀>+t<v>
MUST LIMIT RANGE OF T BECAUSE ITS A LINE SEGMENT
, ◉ Vector form of the equation of a plane
Answer: n•<x-x₀,y-y₀,z-z₀>=0
perpendicular vector • <x-point on plane and n, y-...>
◉ Scalar form of the equation of a plane
Answer: a(x-x₀)+b(y-y₀)+c(z-z₀)=0
x val of perpendicular vector (x-x point on plane and n) + ...
◉ SOLVE
Equation of plane through point (a,b,c) and perpendicular to
n=<d,e,f>
Answer: <d,e,f> • <x-a,y-b,z-c> = 0
d(x-a)+e(y-b)+f(z-c)=0
◉ SOLVE
Equation of plane containing points (a,b,c),(d,e,f),(g,h,i)
Answer: Use three points to get two vectors with the same base
point. u=<d-a,e-b,f-c> v=(g-a,h-b,i-c>
Find cross product. This is n.
Use the base point and n.
Plug in: n•<x-x₀,y-y₀,z-z₀>=0
