Vector and Cartesian equations of lines

Vector and Cartesian equations of lines Quiz

Spec F1 · AQA A-Level Further Maths: Quiz

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  1. 1. Which is a direction vector of the line through (1,2,3)(1,2,3) and (4,0,6)(4,0,6)?

    • A. (5,2,9)(5,2,9)
    • B. (3,−2,3)(3,-2,3)
    • C. (3,2,3)(3,2,3)
    • D. (1,2,3)(1,2,3)

  2. 2. Find the Cartesian equation of r=(1,0,2)+λ(3,4,5)\mathbf r=(1,0,2)+\lambda(3,4,5).

    • A. x−13=y4=z−25\frac{x-1}{3}=\frac{y}{4}=\frac{z-2}{5}
    • B. x+13=y4=z+25\frac{x+1}{3}=\frac{y}{4}=\frac{z+2}{5}
    • C. x−31=y−40=z−52\frac{x-3}{1}=\frac{y-4}{0}=\frac{z-5}{2}
    • D. 3(x−1)=4y=5(z−2)3(x-1)=4y=5(z-2)

  3. 3. Which point lies on r=(2,1,0)+λ(1,−1,2)\mathbf r=(2,1,0)+\lambda(1,-1,2)?

    • A. (5,−2,5)(5,-2,5)
    • B. (5,2,6)(5,2,6)
    • C. (5,−2,6)(5,-2,6)
    • D. (3,2,2)(3,2,2)

  4. 4. A line has Cartesian equation x=3, y−12=z+25x=3,\ \frac{y-1}{2}=\frac{z+2}{5}. A direction vector is

    • A. (3,2,5)(3,2,5)
    • B. (0,2,5)(0,2,5)
    • C. (1,2,5)(1,2,5)
    • D. (3,1,−2)(3,1,-2)

  5. 5. Which line is parallel to r=(1,2,3)+λ(2,−4,6)\mathbf r=(1,2,3)+\lambda(2,-4,6)?

    • A. r=(1,2,3)+μ(2,4,6)\mathbf r=(1,2,3)+\mu(2,4,6)
    • B. r=(2,−4,6)+μ(1,1,1)\mathbf r=(2,-4,6)+\mu(1,1,1)
    • C. r=(0,0,1)+μ(−1,2,−3)\mathbf r=(0,0,1)+\mu(-1,2,-3)
    • D. r=(0,0,1)+μ(1,2,3)\mathbf r=(0,0,1)+\mu(1,2,3)

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