Examples and practice
Vectors: lines and perpendicular feet
Back to lessonPractice section 1 · Questions 1–6
Build a line by extending and splitting a displacement · Convert a line through two points without dividing by zero · +4 more
- Build a line by extending and splitting a displacement
- Convert a line through two points without dividing by zero
- Read a common Cartesian parameter and rescale it consistently
- Practise five conversions between vector and Cartesian forms
- Check a point using one consistent parameter
- Find a perpendicular foot, shortest distance and reflected point
Practice section 2 · Questions 7–12
Find point-to-line distance with cross product and projection · Classify eight pairs of lines in a cuboid · +4 more
- Find point-to-line distance with cross product and projection
- Classify eight pairs of lines in a cuboid
- Distinguish parallel, intersecting and skew lines algebraically
- Find the acute angle from line directions
- Find a line intersection and its acute angle
- Combine parallelogram vectors, an internal angle and a nearest point
Practice section 3 · Questions 13–18
Write vector and Cartesian equations without dividing by zero · Recover a point and direction from Cartesian relations · +4 more
- Write vector and Cartesian equations without dividing by zero
- Recover a point and direction from Cartesian relations
- Check membership and a point-to-line distance
- Find the perpendicular foot and reflect a point
- Classify four pairs of spatial lines and find acute angles
- Find the separation of two parallel lines
Practice section 4 · Questions 19–24
Locate a perpendicular foot and reflect a whole line · Interpret parametric lines and zero cross products · +4 more
- Locate a perpendicular foot and reflect a whole line
- Interpret parametric lines and zero cross products
- Use two line parameters, a division ratio and a cross-product area
- Model cable intersections and minimise drilling distance
- Use an intersection to determine an unknown coordinate
- Find an axis crossing and the origin-to-line distance
Practice section 5 · Questions 25–30
Use a diagonal direction for a line and a parallelogram area · Find a perpendicular foot and reflect a point in a line · +4 more
- Use a diagonal direction for a line and a parallelogram area
- Find a perpendicular foot and reflect a point in a line
- Find a projection foot using two methods
- Reflect a point in a line and calculate the resulting area
- Reflect an intersecting line by reflecting one point
- Separate a trigonometric parameter from a later special case
Practice section 6 · Questions 31–33
Prove a rhombus using a perpendicular projection · Intersect extended lines by comparing independent coefficients · +1 more