Vector (Cross) Product & Applications

Grade 12 Maths Higher — Vector (Cross) Product & Applications: 25 practice questions with instant scoring and explanations.

1. Vector (cross) product a × b has direction given by:
2. For 2D vectors in 3D: (a₁, a₂, 0) × (b₁, b₂, 0) =
3. a × b is:
4. a × a =
5. For perpendicular vectors a and b: |a × b| =
6. For parallel vectors a and b: a × b =
7. Cross product satisfies distributivity: a × (b + c) =
8. Unit vectors: i × j =
9. j × k =
10. k × i =
11. For i × i, j × j, k × k:
12. Area of parallelogram with sides a and b is:
13. Area of triangle with sides a and b is:
14. Scalar triple product [a, b, c] = a·(b × c) represents:
15. For vectors a = (1,0,0), b = (0,1,0), c = (0,0,1): [a,b,c] =
16. If three vectors are coplanar, their scalar triple product is:
17. Vector triple product a × (b × c) =:
18. The formula (a × b)·c = a·(b × c) is due to:
19. Torque τ = r × F where r is position and F is force:
20. If a = (1, 2, 3) and b = (4, 5, 6), then a × b =
21. For a and b perpendicular with |a| = 3, |b| = 4:
22. Lagrange's identity: |a × b|² + (a·b)² =
23. If a × b = c and b × c = a, then c × a =
24. The magnitude |a × b| is maximum when a and b are:
25. Review question for Vector (Cross) Product & Applications