If A = 1i + 2j + 3k and B = 4i + 5j + 6k, what is A · B?

If A = 1i + 2j + 3k and B = 4i + 5j + 6k, what is A · B?

Step 1: Identify the components of vector A. A = 1i + 2j + 3k means A has components: A_x = 1, A_y = 2, A_z = 3.
Step 2: Identify the components of vector B. B = 4i + 5j + 6k means B has components: B_x = 4, B_y = 5, B_z = 6.
Step 3: Multiply the corresponding components of A and B. Calculate A_x * B_x = 1 * 4 = 4.
Step 4: Calculate A_y * B_y = 2 * 5 = 10.
Step 5: Calculate A_z * B_z = 3 * 6 = 18.
Step 6: Add the results from Steps 3, 4, and 5 together. So, 4 + 10 + 18 = 32.
Step 7: The final result of A · B is 32.

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