Given vectors A = 2i + 2j and B = 3i + 4j, what is the value of A · B?

Given vectors A = 2i + 2j and B = 3i + 4j, what is the value of A · B?

Step 1: Identify the components of vector A. A = 2i + 2j means A has a component of 2 in the i direction and 2 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 = (2 * 3) + (2 * 4).
Step 5: Calculate the products. 2 * 3 = 6 and 2 * 4 = 8.
Step 6: Add the results of the products together. 6 + 8 = 14.

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