If A = 4i + 3j and B = 4i - 3j, what is A · B?

If A = 4i + 3j and B = 4i - 3j, what is 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 = 4i - 3j means B has a component of 4 in the i direction and -3 in the j direction.
Step 3: Use the formula for the dot product A · B, which is A · B = (A_i * B_i) + (A_j * B_j).
Step 4: Substitute the components into the formula. A_i = 4, B_i = 4, A_j = 3, B_j = -3.
Step 5: Calculate the dot product: (4 * 4) + (3 * -3).
Step 6: Perform the multiplication: 4 * 4 = 16 and 3 * -3 = -9.
Step 7: Add the results from the multiplication: 16 + (-9) = 16 - 9.
Step 8: Simplify the final result: 16 - 9 = 7.

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 the components of vectors in terms of i (horizontal) and j (vertical) directions is crucial for performing vector operations.