If A = 7i - 3j and B = -2i + 5j, what is the value of A · B?

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Question: If A = 7i - 3j and B = -2i + 5j, what is the value of A · B?

Options:

Correct Answer: -29

Solution:

A · B = (7)(-2) + (-3)(5) = -14 - 15 = -29.

If A = 7i - 3j and B = -2i + 5j, what is the value of A · B?

If A = 7i - 3j and B = -2i + 5j, what is the value of A · B?

Step 1: Identify the components of vector A. A = 7i - 3j means A has a component of 7 in the i direction and -3 in the j direction.
Step 2: Identify the components of vector B. B = -2i + 5j means B has a component of -2 in the i direction and 5 in the j direction.
Step 3: Use the formula for the dot product A · B, which is 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) * (-2) + (-3) * (5).
Step 5: Calculate the first part: (7) * (-2) = -14.
Step 6: Calculate the second part: (-3) * (5) = -15.
Step 7: Add the results from Step 5 and Step 6: -14 + (-15) = -14 - 15.
Step 8: Final calculation: -14 - 15 = -29.

Dot Product of Vectors – The dot product of two vectors A and B is calculated by multiplying their corresponding components and summing the results.