Topic overview
Long vector questions often stack intersection, perpendicularity, distance and positional constraints together. Every verbal condition should be converted into an independent equation.
Key concepts
Write the line as . For intersection, set the three coordinates equal; for perpendicularity, use zero dot product; the shortest vector from a point to a line is perpendicular to the direction vector.
Key points
- ◆Do not mix up the parameters
- ◆The three coordinate equations must be compatible
- ◆Distance must be taken as the magnitude of the vector
Worked examples
Try each example yourself before checking the explanation.
1foot-of-perpendicular parameter
What is the parameter of the foot of the perpendicular from point to the line ?
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