If A = 7i + 1j and B = 1i + 7j, calculate A · B.

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Question: If A = 7i + 1j and B = 1i + 7j, calculate A · B.

Options:

Correct Answer: 56

Solution:

A · B = (7)(1) + (1)(7) = 7 + 7 = 14.

If A = 7i + 1j and B = 1i + 7j, calculate A · B.

If A = 7i + 1j and B = 1i + 7j, calculate A · B.

Step 1: Identify the components of vector A. A = 7i + 1j means A has a component of 7 in the i direction and 1 in the j direction.
Step 2: Identify the components of vector B. B = 1i + 7j means B has a component of 1 in the i direction and 7 in the j direction.
Step 3: To calculate the dot product A · B, use the formula: A · B = (A's i component) * (B's i component) + (A's j component) * (B's j component).
Step 4: Substitute the values into the formula: A · B = (7) * (1) + (1) * (7).
Step 5: Calculate the first part: (7) * (1) = 7.
Step 6: Calculate the second part: (1) * (7) = 7.
Step 7: Add the results from Step 5 and Step 6: 7 + 7 = 14.

Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.
Vector Representation – Understanding how to represent vectors in terms of their components along the i and j axes.