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Lesson Packs · Grade 12 · Mathematics

Vectors in Space: Dot and Cross Product

Students work with vectors in three dimensions: component form, magnitude and unit vectors, the dot product and the angle between two vectors, the perpendicular test, and the cross product with its use for areas of parallelograms and triangles.

Unit 6 · Lesson 19 · Vectors and 3D Geometry

Preview

Vectors in Space: Dot and Cross Product — Slide 1
  • Vectors in Space: Dot and Cross Product — Slide 4
    Slide 4
  • Vectors in Space: Dot and Cross Product — Slide 7
    Slide 7
  • Vectors in Space: Dot and Cross Product — Slide 16
    Slide 16
  • Vectors in Space: Dot and Cross Product — Slide 17
    Slide 17
  • Vectors in Space: Dot and Cross Product — Worksheet, page 1
    Worksheet, page 1
  • Vectors in Space: Dot and Cross Product — Answer key, page 1
    Answer key, page 1

Learning objectives

  • Write vectors in space in component form, and find their magnitudes and unit vectors.
  • Calculate the dot product and use it to find the angle between two vectors and to test whether they are perpendicular.
  • Calculate the cross product and use it to find the areas of parallelograms and triangles.

What's inside

  • 37 PowerPoint slides: lesson, worked examples and the worksheet with solutions
  • 10 worksheet questions (32 marks) with step-by-step solutions
  • Printable worksheet (3 pages) and a teacher answer key
  • Fully editable in PowerPoint, Google Slides, Keynote and Word

More lessons in this unit

Questions teachers ask

Can I edit the files?

Yes. The PowerPoint and the Word worksheet are fully editable, so you can change examples, add questions or adapt the design for your class.

How do I use the worksheet slides?

After the teaching slides, each worksheet question appears on its own slide. Let students try it first, then show the next slide and work through the solution together.

Is there an answer key?

Yes. The Word file ends with a teacher answer key that has the answer and a worked solution for every question. It is also included as a separate PDF.

Which languages are available?

Every Lesson Pack is made in 18 languages: English, Simplified Chinese, Hindi, Spanish, Arabic, French, Bengali, Portuguese, Indonesian, Urdu, Vietnamese, Albanian, Italian, German, Turkish, Malay, Greek and Traditional Chinese (Hong Kong).

Do downloads count toward my plan?

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