If A = i + 2j + 3k and B = 4i + 5j + 6k, find A · B.
Practice Questions
1 question
Q1
If A = i + 2j + 3k and B = 4i + 5j + 6k, find A · B.
32
30
28
34
A · B = (1)(4) + (2)(5) + (3)(6) = 4 + 10 + 18 = 32.
Questions & Step-by-step Solutions
1 item
Q
Q: If A = i + 2j + 3k and B = 4i + 5j + 6k, find A · B.
Solution: A · B = (1)(4) + (2)(5) + (3)(6) = 4 + 10 + 18 = 32.
Steps: 7
Step 1: Identify the components of vector A. A = i + 2j + 3k means A has components: 1 (for i), 2 (for j), and 3 (for k).
Step 2: Identify the components of vector B. B = 4i + 5j + 6k means B has components: 4 (for i), 5 (for j), and 6 (for k).
Step 3: Use the formula for the dot product A · B, which is calculated as (A's i component * B's i component) + (A's j component * B's j component) + (A's k component * B's k component).
Step 4: Substitute the values into the formula: (1 * 4) + (2 * 5) + (3 * 6).
