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✦ Class 12 · Maths
Vectors
You'll see how a simple arrow can solve real‑world problems.
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What this lesson covers
Step by step, in this order.
- 1A vector has magnitude and direction, drawn as an arrow.
- 2Magnitude is the size, measured in metres for displacement.
- 3A scalar has only magnitude, like temperature in degrees Celsius.
- 4A position vector joins the origin to a point in space.
- 5A unit vector has length one; for (1,2,2) it is (1/3,2/3,2/3).
- 6Vector addition uses tip‑to‑tail or the parallelogram law.
- 7Scaling a vector multiplies each component; 3·(2,‑1) = (6,‑3).
- 8Dot product a·b = |a||b|cosθ, gives work in joules.
- 9Cross product a×b = |a||b|sinθ n̂, gives torque in newton‑metre; Gibbs introduced it in 1880s.
- 10TRY IT: two forces 30 N at 60° – find resultant step by step.
How it looks
A real board, not a video.
This board is from a different Maths lesson — yours will look like this. She writes and draws while she explains, and stops to check you followed.
Doubts this lesson clears up
- What does magnitude mean for a vector?
- How do I find a unit vector from any vector?
- Why does a zero dot product mean perpendicular?
- How does the cross product give the area of a triangle?
- What happens to a vector when multiplied by a negative number?
- Can you give everyday examples of dot and cross products?
Class 12 Maths
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