Step 1: Identify the components of vector A. A = 1i + 1j means A has a component of 1 in the i direction and 1 in the j direction.
Step 2: Identify the components of vector B. B = 1i + 1j means B has a component of 1 in the i direction and 1 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 = 1, B_i = 1, A_j = 1, B_j = 1.
Step 5: Calculate the dot product. A · B = (1 * 1) + (1 * 1).
Step 6: Perform the multiplication. This gives us 1 + 1.
Step 7: Add the results together. 1 + 1 = 2.
Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.
Vector Representation – Understanding how vectors are represented in terms of their components (i and j) is crucial for performing operations like the dot product.
