If A = (a, b, c) and B = (1, 2, 3), and A · B = 14, what is the equation?
Correct Answer: a + 2b + 3c = 14
- Step 1: Identify the vectors A and B. A = (a, b, c) and B = (1, 2, 3).
- Step 2: Understand that A · B means the dot product of A and B.
- Step 3: Write the formula for the dot product: A · B = a*1 + b*2 + c*3.
- Step 4: Substitute the values from the vectors into the formula: A · B = a*1 + b*2 + c*3.
- Step 5: Set the equation equal to 14, as given: a*1 + b*2 + c*3 = 14.
- Dot Product – The dot product of two vectors is calculated by multiplying corresponding components and summing the results.
- Vector Notation – Understanding how to represent vectors and their components is crucial for solving problems involving vector operations.
