CBSE · Class 12 · Mathematics · Chapter 10

Vector Algebra

Vectors and vector operations.

9 lessons 130 min
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Lessons in this chapter

  1. 1Understanding Vectors in SpaceLearn how magnitude and direction work together to describe vectors and locate points in space.
  2. 2Adding and Scaling VectorsBuild vector sums and differences geometrically, and see how scalar multiplication changes an arrow.
  3. 3Vector Components and DirectionTranslate geometric arrows into components, then calculate magnitudes, unit vectors and direction information.
  4. 4Vectors Between Points and the Section FormulaUse position-vector differences to describe segments, divide them in a ratio and investigate shapes.
  5. 5The Dot Product and AnglesMeasure directional alignment with a scalar product, and use it to calculate angles and test perpendicularity.
  6. 6Projections and Dot Product ApplicationsUse projections and dot-product identities to resolve vectors, calculate lengths and explain geometric inequalities.
  7. 7The Cross Product and OrientationUnderstand the magnitude and direction of a vector product using right-handed orientation.
  8. 8Calculating Cross Products and AreasCalculate vector products in components and use their magnitudes to find perpendicular unit vectors and areas.
  9. 9Chapter Summary and PracticeConnect the whole chapter and practise choosing between geometric constructions, components, projections and vector products.
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