For vectors A = 4i + 3j and B = 3i - 4j, find A · B.

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Question: For vectors A = 4i + 3j and B = 3i - 4j, find A · B.

Options:

Correct Answer: -6

Solution:

A · B = (4)(3) + (3)(-4) = 12 - 12 = 0.

For vectors A = 4i + 3j and B = 3i - 4j, find A · B.

For vectors A = 4i + 3j and B = 3i - 4j, find A · B.

Step 1: Identify the components of vector A. A = 4i + 3j means A has a component of 4 in the i direction and 3 in the j direction.
Step 2: Identify the components of vector B. B = 3i - 4j means B has a component of 3 in the i direction and -4 in the j direction.
Step 3: Use the formula for the dot product of two vectors. The dot product A · B is calculated as (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 = (4 * 3) + (3 * -4).
Step 5: Calculate the first part: 4 * 3 = 12.
Step 6: Calculate the second part: 3 * -4 = -12.
Step 7: Add the results from Step 5 and Step 6: 12 + (-12) = 0.

Dot Product of Vectors – The dot product of two vectors A and B is calculated as A · B = Ax * Bx + Ay * By, where Ax and Ay are the components of vector A, and Bx and By are the components of vector B.