4.04a-c Vector equations of lines and planes, scalar product Quiz: OCR Further Maths, Unit 1

The 20 questions

1. What is the scalar product of two perpendicular non-zero vectors equal to?

   • 0
   • -1
   • 1
   • Infinite

2. In the vector equation of a line r = a + t b, what does b represent?

   • Position vector
   • Direction vector
   • Perpendicular distance
   • Normal vector

3. In the vector equation of a plane r . n = d, what does n represent?

   • Normal vector
   • Direction vector
   • Position vector
   • Tangent vector

4. What is the scalar product of vectors (1, 2, 3) and (4, -1, 2)?

   • 4
   • 8
   • 10
   • 12

5. Which of these vector equations represents a plane through the origin?

   • r x n = 0
   • r . n = 1
   • r = a + t b
   • r . n = 0

6. How many independent parameters are needed in the vector equation of a plane?

   • Two
   • Three
   • Zero
   • One

7. What is the angle between two vectors if their scalar product equals the product of their magnitudes?

   • 0 degrees
   • 90 degrees
   • 180 degrees
   • 45 degrees

8. Calculate the scalar product of the vector (3, 0, -4) with itself.

   • 5
   • -7
   • 25
   • 7

9. What form does the Cartesian equation of a line in three dimensions take?

   • Quadratic equation
   • Single linear equation
   • Symmetric fractions
   • Matrix product

10. What is the x-coordinate where the line r = (1,0,2) + t(2,1,-1) intersects the plane z = 0?

    • 5
    • 3
    • 1
    • 4

11. What is the geometric relationship between two lines that are not parallel and do not intersect?

    • Perpendicular lines
    • Coincident lines
    • Skew lines
    • Coplanar lines

12. What is the scalar product of (2, -3, 1) and (1, 1, 1)?

    • 2
    • 6
    • 0
    • -1

13. What does the Cartesian equation ax + by + cz = d represent in 3D space?

    • A line
    • A sphere
    • A point
    • A plane

14. Find the distance from the origin to the plane r . (2, -1, 2) = 9.

    • 81
    • 9
    • 3
    • 4.5

15. What is the cosine of the angle between planes r . (1,1,0) = 2 and r . (0,1,1) = 5?

    • 0.25
    • 0.5
    • 1
    • 0

16. What is the shortest distance between parallel planes r . (1,2,2) = 3 and r . (1,2,2) = 12?

    • 4
    • 3
    • 1
    • 9

17. Which formula finds the acute angle θ between a line with direction d and plane with normal n?

    • sin(θ) = |d x n| / (|d||n|)
    • tan(θ) = |d . n| / (|d||n|)
    • sin(θ) = |d . n| / (|d||n|)
    • cos(θ) = |d . n| / (|d||n|)

18. Where does the line r = t(1, 2, 3) intersect the plane x + y + z = 12?

    • (1, 2, 3)
    • (4, 8, 12)
    • (2, 4, 6)
    • (3, 6, 9)

19. If line r = (1, 2, 3) + t(2, -1, k) is perpendicular to vector (3, 2, 2), what is k?

    • 1
    • 2
    • -2
    • -4

20. What is the perpendicular distance from point (1, 0, 0) to plane r . (0, 3, 4) = 12?

    • 12
    • 2
    • 3
    • 2.4

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