If A = 2i + 2j and B = 2i - 2j, find A · B. (2021)

If A = 2i + 2j and B = 2i - 2j, find A · B. (2021)

Step 1: Identify the vectors A and B. A = 2i + 2j and B = 2i - 2j.
Step 2: Write down the formula for the dot product of two vectors. The dot product A · B = (A_x * B_x) + (A_y * B_y), where A_x and A_y are the components of vector A, and B_x and B_y are the components of vector B.
Step 3: Identify the components of A and B. For A, A_x = 2 and A_y = 2. For B, B_x = 2 and B_y = -2.
Step 4: Substitute the components into the dot product formula: A · B = (2 * 2) + (2 * -2).
Step 5: Calculate the first part: 2 * 2 = 4.
Step 6: Calculate the second part: 2 * -2 = -4.
Step 7: Add the results from Step 5 and Step 6: 4 + (-4) = 0.

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 and j components is crucial for performing vector operations.