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

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

Step 1: Identify the components of vector A. A = 3i + 4j means A has a component of 3 in the i direction and 4 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 of two vectors. The dot product A · B is calculated as (A_i * B_i) + (A_j * B_j).
Step 4: Substitute the values into the formula. A_i = 3, B_i = 4, A_j = 4, B_j = 3.
Step 5: Calculate the first part of the dot product: (3 * 4) = 12.
Step 6: Calculate the second part of the dot product: (4 * 3) = 12.
Step 7: Add the two results together: 12 + 12 = 24.
Step 8: Conclude that the value of A · B is 24.

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