Vector equations of lines

Vector equations of lines Quiz

Spec 7.6 · Edexcel International A Level Maths: Quiz

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5 questions, one answer each

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  1. 1. Which is a vector equation of the line through A(1,0,2)A(1,0,2) and B(3,1,−1)B(3,1,-1)?

    • A. r=(3,1,−1)+t(1,0,2)\mathbf{r}=(3,1,-1)+t(1,0,2)
    • B. r=(1,0,2)+t(4,1,1)\mathbf{r}=(1,0,2)+t(4,1,1)
    • C. r=(1,0,2)+t(2,1,−3)\mathbf{r}=(1,0,2)+t(2,1,-3)
    • D. r=(2,1,−3)+t(1,0,2)\mathbf{r}=(2,1,-3)+t(1,0,2)

  2. 2. A line has equation r=(1,2,0)+t(2,−1,4)\mathbf{r}=(1,2,0)+t(2,-1,4). Which line is parallel to it?

    • A. r=(1,2,0)+s(2,1,4)\mathbf{r}=(1,2,0)+s(2,1,4)
    • B. r=(2,−1,4)+s(1,2,0)\mathbf{r}=(2,-1,4)+s(1,2,0)
    • C. r=(0,0,0)+s(4,−2,4)\mathbf{r}=(0,0,0)+s(4,-2,4)
    • D. r=(0,0,0)+s(−4,2,−8)\mathbf{r}=(0,0,0)+s(-4,2,-8)

  3. 3. Does (5,−1,7)(5,-1,7) lie on r=(1,3,−1)+t(2,−2,4)\mathbf{r}=(1,3,-1)+t(2,-2,4)?

    • A. No, since xx and yy give different values of tt
    • B. Yes, when t=2t=2
    • C. Yes, when t=4t=4
    • D. No, since zz gives a different value of tt

  4. 4. Two lines in three dimensions are skew when

    • A. there is no pair of values of the parameters satisfying all three component equations, and the directions are not parallel
    • B. their direction vectors are parallel
    • C. they cross at one point
    • D. they have the same direction vector

  5. 5. Lines r=(1,0,2)+s(1,1,1)\mathbf{r}=(1,0,2)+s(1,1,1) and r=(4,1,2)+t(−1,1,2)\mathbf{r}=(4,1,2)+t(-1,1,2) intersect. Find the point.

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

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