Consider the two robots “Afoa” and “Bromich”. They move in straight lines at constant speeds. Their paths will be the straight lines A and B, where t ₁ , t ₂ ∈ R.

A : (x, y) = (0, 5) + t ₁ (4, 1)

B : (x, y) = (40, 0) + t ₂ (-2, 2)

(a) Show how the Matrix equation below is applicable to finding the intersection point of the robots.

4 ……………… 2 t ₁ = 40

1 ……………… -2 t ₂ = -5

(b) Solve the matrix equation using an inverse matrix. Use your solutions to find the point where the lines intersect.

(c) A 3 ^rd robot, “Cronk”, wants to take a path that intersects the other two paths, at the same point that they intersect. It’s path is given by.

C : (x, y) = (10, 60) + t ₃ v t ₃ ∈ R

Give any two vectors for v, that allow A, B, C to intersect at this point.

(d) Lets use t = time as the parameter in all 3 question, t = 0 is when the robots are at their starting positions (0, 5), (40, 0) and (10, 60). Find vector v ₁ , v ₂ , v ₃ , that would mean Afoa, Bromich and Cronk collide simultaneously at the same point as before.

A : (x, y) = (0, 5) + tv ₁

B : (x, y) = (40, 0) + tv ₂

C : (x, y) = (10, 60) + tv ₃

Answer rating: 100% (QA)

a By given conditions we have 05 t 1 4 1 400 t 2 2 2 ie 0 4t 1 40 2t 2 5 ... View the full answer