Tip to tail
"Tip to tail" is a free, interactive Class 12 Maths simulation for JEE, built on the lesson "Adding vectors" in Vector Algebra. Orange a is the drone's airspeed and blue b is the wind, in m/s on a grid with east to the right and north up. It starts at a = 4ĵ (north) and b = 3î (east). The green arrow is the ground velocity a + b. Switch views: the triangle, the parallelogram and b-then-a all end at the same green tip. A + b is the arrow from the tail of a to the head of b when b starts at the head of a. The parallelogram law gives the same arrow, a + b = b + a, and |a + b| ≤ |a| + |b| with equality only for vectors pointing the same way. JEE Main asked 55 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Adding vectors in Vector Algebra. Change the values and watch what happens.
In JEE Main
42 shifts analysed
55 questions from Vector Algebra across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §10.4
- Triangle law: to add a and b, draw b starting at the head of a. The vector from the tail of a to the head of b is a + b. A trip from A to B and then B to C has the same net effect as AC, so AB + BC = AC.
- Going round a closed triangle gives nothing: AB + BC + CA = 0, since the path ends where it began.
- Subtraction is adding the negative: a − b = a + (−b). For example AC − BC = AC + CB = AB.
- Parallelogram law: draw a and b from one point and complete the parallelogram; the diagonal from that point is a + b. It gives the same vector as the triangle law.
- Addition is commutative, a + b = b + a, and associative, (a + b) + c = a + (b + c), so a sum of several vectors can be written without brackets. Also a + 0 = a and a + (−a) = 0.
- Example with numbers: a drone flies at 4 m/s due north through air that drifts 3 m/s due east. Its velocity over the ground is 3î + 4ĵ, of speed √(9 + 16) = 5 m/s, heading tan⁻¹(3/4) ≈ 36.9° east of north.
Questions
3 answers
- What does the "Tip to tail" simulation show?
- Orange a is the drone's airspeed and blue b is the wind, in m/s on a grid with east to the right and north up. It starts at a = 4ĵ (north) and b = 3î (east). The green arrow is the ground velocity a + b. Switch views: the triangle, the parallelogram and b-then-a all end at the same green tip.
- Does JEE Main ask questions from Vector Algebra?
- Yes. JEE Main asked 55 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Adding vectors" in Vector Algebra (Class 12 Maths).
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