Intersections and distances involving planes

Intersections and distances involving planes Quiz

Spec F6 · AQA A-Level Further Maths: Quiz

Studying this course? Keep your progress in one place.

Pick an answer for each. Quizzes never use energy.

5 questions, one answer each

Each answer is checked as you go, with why.

See all 5 questions

  1. 1. Find the point where r=(1,2,3)+t(1,1,1)\mathbf r=(1,2,3)+t(1,1,1) meets x+y+z=12x+y+z=12.

    • A. (1,2,3)(1,2,3)
    • B. (3,4,5)(3,4,5)
    • C. (2,3,4)(2,3,4)
    • D. (4,5,6)(4,5,6)

  2. 2. Find the distance from the origin to the plane 2x+3y+6z=142x+3y+6z=14.

    • A. 22
    • B. 1414
    • C. 1411\frac{14}{11}
    • D. 77

  3. 3. Substituting a line into a plane gives 0t=−40t=-4. What does this show?

    • A. The line lies in the plane
    • B. The line meets the plane at t=−4t=-4
    • C. The line is perpendicular to the plane
    • D. The line is parallel to the plane and does not meet it

  4. 4. Find the distance from (1,1,1)(1,1,1) to the plane 2x+2y+z=−42x+2y+z=-4.

    • A. 11
    • B. 33
    • C. 13\frac13
    • D. 99

  5. 5. Substituting a line into a plane gives 0t=00t=0. What does this show?

    • A. The line is perpendicular to the plane
    • B. The line is parallel to the plane but outside it
    • C. The line lies in the plane
    • D. The line meets the plane at the origin

Quiz