Given A = 3i + 4j and B = 0i + 0j, find A · B.

Given A = 3i + 4j and B = 0i + 0j, find A · B.

Step 1: Identify the components of vector A, which are 3i and 4j.
Step 2: Identify the components of vector B, which are 0i and 0j.
Step 3: Use the formula for the dot product, which is A · B = (Ax)(Bx) + (Ay)(By).
Step 4: Substitute the values into the formula: A · B = (3)(0) + (4)(0).
Step 5: Calculate (3)(0) which equals 0.
Step 6: Calculate (4)(0) which also equals 0.
Step 7: Add the results from Step 5 and Step 6: 0 + 0 = 0.
Step 8: Conclude that A · B = 0.

Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.
Vector Representation – Vectors can be represented in terms of their components along the i and j axes.