NCERT Mathematics, Class 12, textbook pages 338–376 (Part II)

How to help your child with Class 12 Maths Chapter 10, Vector Algebra, at home

Vectors, dot and cross products, explained for parents: a 60-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

3 km east4 km north5 km

NCERT Class 12 Maths Chapter 10 Vector Algebra: what it teaches

Your teen represents quantities with direction as vectors, adds them, finds magnitudes and unit vectors, and uses dot and cross products for angles, projections and areas.

Why it matters later. Vectors are used in 3D geometry, physics (forces) and computer graphics.

See it: this chapter in pictures

|2i + 3j − 6k|√(4 + 9 + 36)= 7
Pythagoras in 3D.
a · b = |a||b| cos θ(i + j) · i = 1θ = 45°
Dot product gives angles.
i × j = kj × k = ik × i = j
Cyclic order is positive.

You need

  • graph paper
  • arrows cut from paper
  • a calculator

Tonight’s 60 minutes

  1. Add two displacement vectors: 3 km east and 4 km north (5 km).
  2. Find the magnitude of 2i + 3j − 6k (7).
  3. Use the dot product to find the angle between i + j and i (45°).
  4. Find the area of a parallelogram with a × b.

Words to use

  • vector
  • magnitude
  • unit vector
  • dot product
  • cross product
  • projection

Watch for

  • Treating vectors like numbers. Keep track of direction; use components.
  • Mixing dot and cross product results. Dot gives a number; cross gives a vector.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

You3 km east, 4 km north: displacement?

Your child√(9 + 16) = 5 km.

A game for this week: Vector walk

  1. Give walking instructions as vectors.
  2. Add them to find displacement.
  3. Walk it out.
  4. Compare distance and displacement.

A 5-day plan, 60 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Forces in physics.
  • Navigation.
  • Game physics.
  • Robotics.

Quick check

Ask these at the end of the week. Tap to see the answer.

|2i + 3j − 6k|?

7.

Angle between i + j and i?

45°.

i × j?

k.

Ready for the next chapter when your child…

  • Adds vectors and finds magnitudes.
  • Uses dot product for angles.
  • Uses cross product for areas.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 12). See the full Class 12 parent guide for every chapter.

Questions parents ask

What is a unit vector?

A vector of length 1 in a given direction.

What does the cross product give?

A vector perpendicular to both, with magnitude equal to the parallelogram area.