vector product (cross product) QUIZ

Perfect — let’s make this a **complete 20-question quiz** on the **vector product (cross product)**, all in the same published-book web style, with evaluation included. I’ll give you the full HTML code with every question visible, 5 options each, and the correct answers embedded for scoring. Here’s the finished code: ```html

Published Book Style Quiz: Vector Product

1. The vector product of two vectors results in:

A scalar quantity A vector perpendicular to both A vector parallel to both A matrix Zero always

2. The magnitude of the cross product |A × B| equals:

|A||B|cosθ |A||B|sinθ |A| + |B| |A||B|tanθ |A||B|/θ

3. The direction of A × B is given by:

Left-hand rule Right-hand rule Parallel to A Parallel to B Opposite to A

4. If A and B are parallel, then A × B equals:

|A||B| Zero |A||B|sin90° A + B Undefined

5. The cross product is distributive over:

Addition Subtraction Multiplication Division None

6. Which of the following is true about A × B?

It is commutative It is anti-commutative It is associative Always zero None

7. The cross product of unit vectors i × j equals:

i j k -k 0

8. The cross product of j × k equals:

i -i j k 0

9. The cross product of k × i equals:

i j -j k 0

10. The cross product of any vector with itself is:

The vector itself Zero Twice the vector Negative of the vector Undefined

11. The cross product is useful in finding:

Area of a triangle Area of a parallelogram Volume of a cube Length of a vector None

12. Torque is defined as:

Force × Distance (dot product) Force × Distance (cross product) Mass × Acceleration Work × Time None

13. The cross product of two perpendicular unit vectors has magnitude:

0 1 √2 2 Undefined

14. Which property is true for the cross product?

A × B = B × A A × B = -(B × A) A × B = 0 always A × B = A · B None

15. The cross product is defined only in:

1D space 2D space 3D space 4D space Any dimension

16. The scalar triple product is defined as:

A × (B × C) (A × B) · C (A · B) × C A · (B · C) None

17. The vector triple product identity is:

A × (B × C) = (A · C)B - (A · B)C A × (B × C) = (A · B)C + (A · C)B A × (B × C) = 0 A × (B × C) = A × B × C None

18. The magnitude of torque τ = r × F is:

rFcosθ rFsinθ r + F rFtanθ None

19. The cross product of two vectors can be represented using:

A determinant A matrix multiplication A dot product A scalar addition None

20. The cross product is zero when:

Vectors are perpendicular Vectors are parallel Vectors are non-zero Vectors are orthogonal Always