Walk the line
"Walk the line" is a free, interactive Class 12 Maths simulation for JEE, built on the lesson "Equation of a line" in Three Dimensional Geometry. The laser beam starts at the floor projector F(1, 2, 0) and runs along 2î + 3ĵ + 6k̂, so every point on it is r = (î + 2ĵ) + λ(2î + 3ĵ + 6k̂). Each λ gives one point: watch x, y and z change together, and the three fractions (x − 1)/2, (y − 2)/3, z/6 stay equal to λ. A line is one point plus every multiple of one direction: r = a + λb. Written coordinate by coordinate that is x = x₁ + λa, y = y₁ + λb, z = z₁ + λc, and removing λ gives (x − x₁)/a = (y − y₁)/b = (z − z₁)/c. JEE Main asked 84 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Equation of a line in Three Dimensional Geometry. Change the values and watch what happens.
In JEE Main
42 shifts analysed
84 questions from Three Dimensional Geometry across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §11.3–11.3.1
- A line is fixed by a point and a direction, or by two points.
- Vector form: the line through the point with position vector a, parallel to b, is r = a + λb. Each real λ gives one point of the line, and every point comes from one λ.
- Writing b = aî + bĵ + ck̂, the three numbers a, b, c serve as direction ratios. Here b is a direction, not a length; do not confuse it with |b|.
- Parametric form: through (x₁, y₁, z₁) with ratios a, b, c, the points are x = x₁ + λa, y = y₁ + λb, z = z₁ + λc.
- Cartesian form: eliminating λ gives (x − x₁)/a = (y − y₁)/b = (z − z₁)/c. With direction cosines in place of ratios it reads (x − x₁)/l = (y − y₁)/m = (z − z₁)/n.
- Through two points with position vectors a and b the line is r = a + λ(b − a).
- Worked: through (5, 2, −4) parallel to 3î + 2ĵ − 8k̂ the line is r = 5î + 2ĵ − 4k̂ + λ(3î + 2ĵ − 8k̂), that is (x − 5)/3 = (y − 2)/2 = (z + 4)/(−8).
- Read the coefficients before quoting ratios: (1 − x)/3 = (x − 1)/(−3) has ratio −3 for x, and (7 − 7x)/3 = (x − 1)/(−3/7).
Questions
3 answers
- What does the "Walk the line" simulation show?
- The laser beam starts at the floor projector F(1, 2, 0) and runs along 2î + 3ĵ + 6k̂, so every point on it is r = (î + 2ĵ) + λ(2î + 3ĵ + 6k̂). Each λ gives one point: watch x, y and z change together, and the three fractions (x − 1)/2, (y − 2)/3, z/6 stay equal to λ.
- Does JEE Main ask questions from Three Dimensional Geometry?
- Yes. JEE Main asked 84 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 "Equation of a line" in Three Dimensional Geometry (Class 12 Maths).
Embed this simulation
Free, with a link back
Teaching this idea? Put the simulation on your own page or LMS with this code.