Discussion questions
Choose a section to work through its questions and solutions. Your progress is shared across pages. Ranges follow collection order; original source labels are kept on each question.
Section 1 · Questions 1–6
Give a direction vector the required magnitude · Use equal vectors and diagonal lengths to identify a quadrilateral · +4 more
- Question 1 · Give a direction vector the required magnitude
- Question 2 · Use equal vectors and diagonal lengths to identify a quadrilateral
- Question 3 · Apply the section formula and preserve vertex order
- Question 4 · Find a perpendicular foot and use it as a triangle height
- Question 5 · Expand dot products using magnitudes and an angle
- Question 6 · Prove a projection formula in two ways
Section 2 · Questions 7–12
Find a normal unit vector and direction cosines · Factor a cross product to get a linear relation · +4 more
- Question 7 · Find a normal unit vector and direction cosines
- Question 8 · Factor a cross product to get a linear relation
- Question 9 · Use cross-product antisymmetry before taking a magnitude
- Question 10 · Reflect the origin across an equal-radius chord
- Question 11 · Solve perpendicularity conditions and compare two area methods
- Question 12 · Connect a cross-product relation to areas and a nonzero linear combination