§-Quick questions
NSWMaths Extension 1Vectors (ME-V1)
Quick questions on Parametric vector equations of lines: point and direction form, parameter elimination, intersections
8short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is a line is a point plus multiples of a direction?Show answer
Start at a known point on the line, with position vector . Pick any non-zero direction vector pointing along the line. Every other point is reached by walking some number of steps along . So a general point has position vector
What are line through two points?Show answer
If a line passes through and , a direction along it is . So
What is converting to Cartesian form?Show answer
To get a Cartesian equation, write the two component equations and eliminate . If , solve for , then substitute into :
What are intersection of two lines?Show answer
Two lines meet where their position vectors coincide. Use different parameters for the two lines and set them equal:
What is two readings of the parameter?Show answer
The time reading is what makes collision problems different from intersection problems, covered next.
What is direction-vector scaling confusion?Show answer
and are the same direction; the equation can use either, only the parameter values change. Do not treat differently scaled directions as different lines.
What is coincident lines look "parallel but special"?Show answer
Parallel lines can be the same line. Always test a point before declaring "no intersection".
What is collision treated as intersection?Show answer
Paths crossing is not a collision. A collision needs one shared time making both coordinates equal; verify the second coordinate at the time found from the first.