Vector and Cartesian equations of a line

Vector and Cartesian equations of a line Quiz

Spec 6.1 · Edexcel A-Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. Find a direction vector of the line through (1,2,3)(1,2,3) and (4,0,5)(4,0,5).

    • A. (5,2,8)(5,2,8)
    • B. (3,2,2)(3,2,2)
    • C. (3,−2,−2)(3,-2,-2)
    • D. (3,−2,2)(3,-2,2)

  2. 2. Which is a Cartesian equation of r=(1,0,−2)+λ(2,3,4)\mathbf r=(1,0,-2)+\lambda(2,3,4)?

    • A. x−12=y3=z+24\frac{x-1}{2}=\frac{y}{3}=\frac{z+2}{4}
    • B. x+12=y3=z−24\frac{x+1}{2}=\frac{y}{3}=\frac{z-2}{4}
    • C. x−12=y3=z−24\frac{x-1}{2}=\frac{y}{3}=\frac{z-2}{4}
    • D. x−21=y−30=z−4−2\frac{x-2}{1}=\frac{y-3}{0}=\frac{z-4}{-2}

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

    • A. identical
    • B. intersecting at one point
    • C. parallel but distinct
    • D. skew

  4. 4. What is true of two skew lines?

    • A. They are parallel
    • B. They never meet and are not parallel
    • C. They meet at one point
    • D. They are the same line

  5. 5. Does (3,5,7)(3,5,7) lie on r=(1,1,1)+λ(1,2,3)\mathbf r=(1,1,1)+\lambda(1,2,3)?

    • A. No, xx and yy disagree
    • B. No, zz disagrees
    • C. Yes, with λ=1\lambda=1
    • D. Yes, with λ=2\lambda=2

Quiz