Vectors can be used to solve quite complex problems, in this activity students use position vectors to describe points on the Cartesian plane. Students explore three points located on the function y = 1/x forming a triangle with interesting properties.
- Use position vectors to represent points
- Add and subtract vectors in component form
- Determine the dot product of two vectors
- Determine the magnitude of a vector
- Solve problems with vectors
- Component form of a vector
- Dot Product
- Scalar Product
About the Lesson
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Vectors in component form are used to represent points on the Cartesian plane. Three points in this problem are attached to the function y = 1/x,. Students use the magnitude of the vectors to compute the perimeter and area of the triangle formed. Finding vectors for the altitudes of the triangle and projections of these vectors using scalar multiples produces an interesting result when students determine the point of intersection of the altitudes.