Lines and planes in three dimensions

Lines and planes in three dimensions Quiz

Spec 5.2–3 · Edexcel International A Level Further Maths: Quiz

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5 questions, one answer each

Each answer is checked as you go, with why.

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  1. 1. The equation (r−a)×b=0(\mathbf{r}-\mathbf{a})\times\mathbf{b}=\mathbf{0} means that r−a\mathbf{r}-\mathbf{a} is

    • A. perpendicular to b\mathbf{b}
    • B. parallel to b\mathbf{b}
    • C. equal to b\mathbf{b}
    • D. parallel to a\mathbf{a}

  2. 2. The distance from the origin to the plane r⋅(i+2j+2k)=9\mathbf{r}\cdot(\mathbf{i}+2\mathbf{j}+2\mathbf{k})=9 is

    • A. 99
    • B. 11
    • C. 95\frac{9}{5}
    • D. 33

  3. 3. A direction vector of the line of intersection of x+y+z=1x+y+z=1 and x−y=0x-y=0 is

    • A. i+j−2k\mathbf{i}+\mathbf{j}-2\mathbf{k}
    • B. i−j\mathbf{i}-\mathbf{j}
    • C. i+j+k\mathbf{i}+\mathbf{j}+\mathbf{k}
    • D. i+j+2k\mathbf{i}+\mathbf{j}+2\mathbf{k}

  4. 4. The distance from (1,1,1)(1,1,1) to the plane 2x−2y+z=72x-2y+z=7 is

    • A. 66
    • B. 23\frac23
    • C. 22
    • D. 83\frac{8}{3}

  5. 5. Which must be checked to show two lines are skew?

    • A. they are parallel
    • B. they are not parallel and do not meet
    • C. they meet at one point
    • D. they have equal direction vectors

Quiz