Answer: cos(theta) = 24/25.
- A cos(theta) = 0
- B cos(theta) = 7/25
- C cos(theta) = 1
- D cos(theta) = 24/25
Correct answer: D. cos(theta) = 24/25
Explanation: Dot product: a·b = 3(4)+4(3) = 12+12 = 24. Magnitudes: |a| = √(9+16) = 5, |b| = √(16+9) = 5. cosθ = 24/(5×5) = 24/25. Answer: cosθ = 24/25.
Triangle law of vector addition: placing vector b at the head of vector a, the diagonal from the start to the final head gives the resultant a + b.
Concept context
Vectors, dot product, cross product, and geometric applications