Scalar (Dot) Product & Properties

Grade 12 Maths Higher — Scalar (Dot) Product & Properties: 25 practice questions with instant scoring and explanations.

1. Scalar (dot) product a·b is defined as:
2. If a = (1, 2, 3) and b = (4, 5, 6), then a·b =
3. For perpendicular vectors, a·b =
4. The angle θ between vectors a and b is given by:
5. For parallel vectors a and b: a·b =
6. For antiparallel vectors: a·b =
7. Dot product satisfies commutativity: a·b =
8. Distributive property: a·(b + c) =
9. For scalar k: k(a·b) =
10. a·a =
11. The angle between vectors (1, 0, 0) and (0, 1, 0) is:
12. For unit vectors: i·i = j·j = k·k =
13. Cross products of unit vectors: i·j =
14. Projection of a onto b is:
15. Work done W = F·d where F is force and d is displacement:
16. If a·b = a·c and a ≠ 0, then:
17. Cauchy-Schwarz inequality: |a·b| ≤
18. The angle between a = (2, 0) and b = (0, 3) is:
19. For |a| = 3, |b| = 4, and a·b = 6, angle θ is:
20. Component of a in direction of b is:
21. Triangle inequality for magnitudes: |a + b| ≤
22. For vectors a and b: (a + b)·(a - b) =
23. The formula |a + b|² = |a|² + |b|² + 2a·b is:
24. If a = (1, 2, 2), then a·a =
25. Review question for Scalar (Dot) Product & Properties