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Long answer·Challenge (5/5)·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

Show that L1:r⃗=(1,0,0)+λ(1,−1,1)L_1:\vec r=(1,0,0)+\lambda(1,-1,1) and L2:r⃗=(0,2,1)+μ(2,1,−1)L_2:\vec r=(0,2,1)+\mu(2,1,-1) are skew lines and find their shortest distance.
Total: 5 marks

(a) Show that the lines are not parallel. (1 mark)

(b) Show that the lines do not intersect. (1 mark)

(c) Find the shortest distance. (3 marks)

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cbse-math-12.u4.t4-6.laq.004

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