Does the entire line lie in the plane?
- Use acute line/plane angles; normals must be nonzero and distances nonnegative.
Skills and prerequisite lessons
Working and explanation
BUILD THE REASONING
Hint 1
Use the dot product to connect coordinates with length or angle.
Hint 2
n·u=0 and the initial point is in the plane.
Worked solution
Use the dot product to connect coordinates with length or angle.
Apply the stated relation and retain its conditions.
Direction parallelism plus an incident point proves containment.
The requested relation or conclusion is shown below.
Checks and common pitfalls: Direction parallelism plus an incident point proves containment.
Reasoning checklist · self / teacher assessment
- State a valid definition or model and its assumptions.
- Show the intermediate mathematical relations, not only the final claim.
- Check exclusions, units or the interpretation of the result.
Think first. Reveal a hint when the class is ready.