4.04e-h Vector product, intersections and shortest distances Quiz: OCR Further Maths, Unit 1

The 20 questions

1. What is the result of the vector product of any vector with itself?

   • Zero vector
   • Scalar zero
   • Original vector
   • Unit vector

2. Which expression is equal to the vector product a cross b?

   • b cross a
   • -b cross a
   • -a dot b
   • a dot b

3. What geometric quantity does the magnitude of vector a cross vector b represent?

   • Line length
   • Parallelepiped volume
   • Triangle area
   • Parallelogram area

4. Which formula gives the area of a triangle formed by vectors a and b?

   • 0.5|a cross b|
   • |a dot b|
   • |a cross b|
   • 0.5|a dot b|

5. What geometric quantity is calculated by the absolute scalar triple product of three vectors?

   • Tetrahedron volume
   • Parallelogram area
   • Parallelepiped volume
   • Pyramid area

6. What fraction of the scalar triple product gives the volume of a tetrahedron?

   • One sixth
   • One half
   • One third
   • One quarter

7. What is the value of the scalar triple product if three vectors are coplanar?

   • 1
   • Infinity
   • 0
   • -1

8. In what direction relative to both vectors does their cross product point?

   • Perpendicular
   • At 45 degrees
   • Parallel
   • Tangential

9. In a standard right-handed system, what is the result of unit vector i cross unit vector j?

   • 0
   • 1
   • k
   • -k

10. What is the magnitude of the vector product of two perpendicular unit vectors?

    • 0
    • 0.5
    • 2
    • 1

11. Vectors a and b have magnitude 4 and 6 with angle 30 degrees. What is the triangle area?

    • 24
    • 12
    • 6
    • 3

12. Which vector operation is used in the numerator of the point-to-line shortest distance formula?

    • Matrix inverse
    • Dot product
    • Cross product
    • Scalar addition

13. If the cross product of two non-zero direction vectors is the zero vector, how are lines related?

    • Skew
    • Parallel
    • Perpendicular
    • Intersecting at 90°

14. In the shortest distance formula between skew lines, what operation connects position difference and normal direction?

    • Cross product
    • Vector addition
    • Dot product
    • Scalar division

15. Two parallel planes have equations r dot n = 4 and r dot n = 10, where |n| = 2. What is their distance?

    • 2
    • 14
    • 3
    • 6

16. Two non-parallel lines intersect if and only if the shortest distance between them is what value?

    • -1
    • 0
    • 1
    • Infinity

17. If vector a = (1, 0, 0) and vector b = (0, 2, 3), what is the cross product a cross b?

    • (0, 2, 3)
    • (3, 0, 0)
    • (0, -3, 2)
    • (0, 3, -2)

18. If the volume of a parallelepiped formed by three vectors is 36, what is the volume of the corresponding tetrahedron?

    • 12
    • 6
    • 9
    • 18

19. In a standard right-handed coordinate system, what is the result of unit vector j cross unit vector i?

    • -1
    • 0
    • k
    • -k

20. What is the shortest distance from origin to plane r dot (2i + 2j + k) = 9?

    • 4.5
    • 9
    • 3
    • 1

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