What is the scalar product of the vectors A = 1i + 2j + 3k and B = 4i + 5j + 6k?

What is the scalar product of the vectors A = 1i + 2j + 3k and B = 4i + 5j + 6k?

Step 1: Identify the components of vector A, which are A = 1i + 2j + 3k. This means A has components: A_x = 1, A_y = 2, A_z = 3.
Step 2: Identify the components of vector B, which are B = 4i + 5j + 6k. This means B has components: B_x = 4, B_y = 5, B_z = 6.
Step 3: Use the formula for the scalar product (also known as the dot product) of two vectors: A · B = (A_x * B_x) + (A_y * B_y) + (A_z * B_z).
Step 4: Substitute the values into the formula: A · B = (1 * 4) + (2 * 5) + (3 * 6).
Step 5: Calculate each multiplication: (1 * 4) = 4, (2 * 5) = 10, (3 * 6) = 18.
Step 6: Add the results of the multiplications together: 4 + 10 + 18.
Step 7: Calculate the final sum: 4 + 10 + 18 = 32.

No concepts available.