QCEVault

Vectors in three dimensions — Question 122

Original QCE Vault practice · 6 marks

Q122 · Practice questionTechnology-freeComplex unfamiliar6 marks

QUESTION 122 (6 marks)

The lines l1l_{1}: r=(1,2,0)+s(1,−1,2)r=(1,2,0)+s(1,-1,2) and l2l_{2}: r=(3,0,1)+t(2,1,−1)r=(3,0,1)+t(2,1,-1) are given.
Original diagram for Specialist Mathematics Paper 1 question 12
a)
Show that the lines are skew.
[2 marks]
b)
Find the shortest distance between them.
[2 marks]
c)
Find an equation of the plane containing l1l_{1} and parallel to l2l_{2}.
[2 marks]
Question linkSyllabus coverage

Related questions

  1. Q3 · Original practice · 1 mark
    Original Specialist Mathematics practice question 3: line and plane
    Vectors in three dimensions
  2. Q8 · Original practice · 5 marks
    Original Specialist Mathematics practice question 8: line-plane geometry
    Vectors in three dimensions
  3. Q24 · Original practice · 6 marks
    Let a=(4,−2,4)\mathbf a=(4,-2,4) and b=(1,2,2)\mathbf b=(1,2,2).
    Vectors in three dimensions
  4. Q26 · Original practice · 6 marks
    The sphere x2+y2+z2=9x^2+y^2+z^2=9 is intersected by the line r=(0,0,4)+t(1,0,−1).\mathbf r=(0,0,4)+t(1,0,-1).
    Vectors in three dimensions