Applications of vectors to 3-D geometry

Applications of vectors to 3-D geometry Quiz

Spec 5.3 · Edexcel A-Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. Which point lies on the line x−12=y+3−1=z4\frac{x-1}{2}=\frac{y+3}{-1}=\frac{z}{4}?

    • A. (3,−4,4)(3,-4,4)
    • B. (2,−1,4)(2,-1,4)
    • C. (3,−2,4)(3,-2,4)
    • D. (1,3,0)(1,3,0)

  2. 2. What are the direction cosines of a line with direction ratios 1:2:21:2:2?

    • A. 1, 2, 21,\ 2,\ 2
    • B. 15, 25, 25\frac15,\ \frac25,\ \frac25
    • C. 13, 23, 23\frac13,\ \frac23,\ \frac23
    • D. 19, 49, 49\frac19,\ \frac49,\ \frac49

  3. 3. What does (r−a)×b=0(\mathbf{r}-\mathbf{a})\times\mathbf{b}=\mathbf{0} represent?

    • A. A plane perpendicular to b\mathbf{b}
    • B. A line through a\mathbf{a} parallel to b\mathbf{b}
    • C. A line through a\mathbf{a} perpendicular to b\mathbf{b}
    • D. A sphere centred at a\mathbf{a}

  4. 4. What is the perpendicular distance from the origin to 2x+3y+6z=142x+3y+6z=14?

    • A. 1414
    • B. 77
    • C. 9898
    • D. 22

  5. 5. A line has direction d\mathbf{d} and a plane has normal n\mathbf{n}. Which gives the acute angle θ\theta between them?

    • A. cos⁡θ=∣d⋅n∣∣d∣∣n∣\cos\theta=\frac{|\mathbf{d}\cdot\mathbf{n}|}{|\mathbf{d}||\mathbf{n}|}
    • B. sin⁡θ=∣d⋅n∣∣d∣∣n∣\sin\theta=\frac{|\mathbf{d}\cdot\mathbf{n}|}{|\mathbf{d}||\mathbf{n}|}
    • C. tan⁡θ=∣d⋅n∣∣d∣∣n∣\tan\theta=\frac{|\mathbf{d}\cdot\mathbf{n}|}{|\mathbf{d}||\mathbf{n}|}
    • D. sin⁡θ=∣d×n∣∣d∣∣n∣\sin\theta=\frac{|\mathbf{d}\times\mathbf{n}|}{|\mathbf{d}||\mathbf{n}|}

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