Unit 2 – vector equations of lines and curves

A 10-lesson unit on Further work with vectors, addressing content from Vector equations of lines and curves.

Students build fluency in representing lines, curves, circles, and spheres using vector equations in two and three dimensions. They interpret and construct forms such as r = a + λb and r = p + λ(q − p), exploring direction, parallelism, and collinearity. Through problem solving, they determine intersections, identify skew lines, and link parametric and Cartesian forms to model and graph geometric relationships.

Introduction

Vector equations of lines and curves (DOCX 8.3 MB)

Lesson 1 – gradient and the direction vector

• Gradient and the direction vector (DOCX 4 MB)
• Gradient and the direction vector – slide deck (PPTX 1.6 MB)

Lesson 2 – the vector equation of lines between 2 points

• The vector equation of lines between 2 points (DOCX 3.9 MB)
• The vector equation of lines between 2 points – slide deck (PPTX 1.9 MB)

Lesson 3 – parallel vectors in two and three dimensions

• Parallel vectors in two and three dimensions (DOCX 3.9 MB)
• Parallel vectors in two and three dimensions – slide deck (PPTX 13.9 MB)

Lesson 4 – points on a line and collinearity in vector form

• Points on a line and collinearity in vector form (DOCX 3.9 MB)
• Points on a line and collinearity in vector form – slide deck (PPTX 3.4 MB)

Lesson 5 – relationships between lines

• Relationships between lines (DOCX 4 MB)
• Relationships between lines – slide deck (PPTX 5.8 MB)

Lesson 6 – vector equations of circles

• Vector equations of circles (DOCX 4 MB)
• Vector equations of circles – slide deck (PPTX 3.1 MB)

Lesson 7 – vector and Cartesian equations of curves

• Vector and Cartesian equations of curves (DOCX 3.6 MB)
• Vector and Cartesian equations of curves – slide deck (PPTX 5.7 MB)

Lesson 8 – identifying vector equations of curves in two dimensions

• Identifying vector equations of curves in two dimensions (DOCX 3.9 MB)
• Identifying vector equations of curves in two dimensions – slide deck (PPTX 1.5 MB)

Lesson 9 – identifying vector equations of curves in three dimensions

• Identifying vector equations of curves in three dimensions (DOCX 3.8 MB)
• Identifying vector equations of curves in three dimensions – slide deck (PPTX 7.3 MB)

Lesson 10 – vector equations of spheres

• Vector equations of spheres (DOCX 3 MB)
• Vector equations of spheres – slide deck (PPTX 2 MB)