If A = 6i + 8j and B = 2i + 3j, calculate A · B.

₹0.0

Question: If A = 6i + 8j and B = 2i + 3j, calculate A · B.

Options:

Correct Answer: 36

Solution:

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

If A = 6i + 8j and B = 2i + 3j, calculate A · B.

If A = 6i + 8j and B = 2i + 3j, calculate A · B.

Step 1: Identify the components of vector A. A = 6i + 8j means A has a component of 6 in the i direction and 8 in the j direction.
Step 2: Identify the components of vector B. B = 2i + 3j means B has a component of 2 in the i direction and 3 in the j direction.
Step 3: Multiply the i components of A and B. This means calculate 6 (from A) times 2 (from B), which equals 12.
Step 4: Multiply the j components of A and B. This means calculate 8 (from A) times 3 (from B), which equals 24.
Step 5: Add the results from Step 3 and Step 4 together. So, 12 (from Step 3) plus 24 (from Step 4) equals 36.
Step 6: The final result of A · B is 36.

Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.
Vector Components – Understanding how to break down vectors into their i and j components is essential for performing vector operations.