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Case study·Hard exam skill (4/5)·No calculatorNeeds mentor review

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

Two drone paths are modelled by L1:r⃗=(1,0,0)+λ(2,1,1)L_1:\vec r=(1,0,0)+\lambda(2,1,1) and L2:r⃗=(0,2,1)+μ(1,−1,2).L_2:\vec r=(0,2,1)+\mu(1,-1,2).
Total: 4 marks

(a) State whether the direction vectors are parallel. (1 mark)

(b) Explain whether the paths intersect. (1 mark)

(c) Find the shortest distance between the paths. (2 marks)

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cbse-math-12.u4.t4-6.case.005

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