Intersection of lines and distances

Intersection of lines and distances Quiz

Spec F6 · AQA A-Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. Find the point where r=(1,2,0)+λ(1,1,1)\mathbf r=(1,2,0)+\lambda(1,1,1) meets r=(0,3,3)+μ(1,0,−1)\mathbf r=(0,3,3)+\mu(1,0,-1).

    • A. (1,2,0)(1,2,0)
    • B. (2,3,1)(2,3,1)
    • C. (3,3,1)(3,3,1)
    • D. (0,3,3)(0,3,3)

  2. 2. The lines r=λ(1,1,0)\mathbf r=\lambda(1,1,0) and r=(0,0,1)+μ(1,−1,0)\mathbf r=(0,0,1)+\mu(1,-1,0) are

    • A. parallel
    • B. intersecting at the origin
    • C. intersecting at (0,0,1)(0,0,1)
    • D. skew

  3. 3. Find the distance from (2,3,5)(2,3,5) to the line r=λ(0,0,1)\mathbf r=\lambda(0,0,1).

    • A. 13\sqrt{13}
    • B. 55
    • C. 38\sqrt{38}
    • D. 22

  4. 4. Find the distance between the parallel lines r=λ(1,0,0)\mathbf r=\lambda(1,0,0) and r=(0,6,8)+μ(1,0,0)\mathbf r=(0,6,8)+\mu(1,0,0).

    • A. 1414
    • B. 66
    • C. 1010
    • D. 88

  5. 5. PP and QQ lie on two skew lines with directions d1\mathbf d_1, d2\mathbf d_2, and PQPQ is the shortest distance. Which is true?

    • A. PQ→⋅d1=1\overrightarrow{PQ}\cdot\mathbf d_1=1
    • B. PQ→⋅d1=0\overrightarrow{PQ}\cdot\mathbf d_1=0 and PQ→⋅d2=0\overrightarrow{PQ}\cdot\mathbf d_2=0
    • C. PQ→\overrightarrow{PQ} is parallel to d1\mathbf d_1
    • D. d1⋅d2=0\mathbf d_1\cdot\mathbf d_2=0 always

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