If A = 1i + 1j + 1k and B = 1i + 1j + 1k, what is A · B?

If A = 1i + 1j + 1k and B = 1i + 1j + 1k, what is A · B?

Step 1: Identify the vectors A and B. A = 1i + 1j + 1k and B = 1i + 1j + 1k.
Step 2: Write down the components of A and B. Both A and B have components: A = (1, 1, 1) and B = (1, 1, 1).
Step 3: Use the formula for the dot product: 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 * 1) + (1 * 1) + (1 * 1).
Step 5: Calculate each multiplication: (1 * 1) = 1, (1 * 1) = 1, (1 * 1) = 1.
Step 6: Add the results together: 1 + 1 + 1 = 3.

Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.
Vector Notation – Understanding the representation of vectors in terms of their components along the i, j, and k axes.