Question: If A = 7i + 1j and B = 1i + 7j, find A · B.
Options:
56
14
8
50
Correct Answer: 56
Solution:
A · B = (7)(1) + (1)(7) = 7 + 7 = 14.
If A = 7i + 1j and B = 1i + 7j, find A · B.
Practice Questions
Q1
If A = 7i + 1j and B = 1i + 7j, find A · B.
56
14
8
50
Questions & Step-by-Step Solutions
If A = 7i + 1j and B = 1i + 7j, find A · B.
Step 1: Identify the components of vector A, which are 7i and 1j.
Step 2: Identify the components of vector B, which are 1i and 7j.
Step 3: Multiply the i components of A and B together: 7 (from A) * 1 (from B) = 7.
Step 4: Multiply the j components of A and B together: 1 (from A) * 7 (from B) = 7.
Step 5: Add the results from Step 3 and Step 4 together: 7 + 7 = 14.
Step 6: The final result of A · B is 14.
Dot Product – The dot product of two vectors A and B is calculated by multiplying their corresponding components and summing the results.
Vector Components – Understanding how to break down vectors into their i (x-axis) and j (y-axis) components is essential for calculating the dot product.
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