If A = 2i + 3j and B = 4i + 0j, what is the value of A · B? (2022)

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Question: If A = 2i + 3j and B = 4i + 0j, what is the value of A · B? (2022)

Options:

Correct Answer: 8

Exam Year: 2022

Solution:

A · B = (2)(4) + (3)(0) = 8 + 0 = 8

If A = 2i + 3j and B = 4i + 0j, what is the value of A · B? (2022)

If A = 2i + 3j and B = 4i + 0j, what is the value of A · B? (2022)

Step 1: Identify the components of vector A. A = 2i + 3j means A has a component of 2 in the i direction and a component of 3 in the j direction.
Step 2: Identify the components of vector B. B = 4i + 0j means B has a component of 4 in the i direction and a component of 0 in the j direction.
Step 3: Use the formula for the dot product A · B, which is (A_i * B_i) + (A_j * B_j).
Step 4: Substitute the values into the formula. A_i = 2, B_i = 4, A_j = 3, B_j = 0.
Step 5: Calculate the dot product: (2 * 4) + (3 * 0).
Step 6: Perform the multiplication: 2 * 4 = 8 and 3 * 0 = 0.
Step 7: Add the results from the multiplication: 8 + 0 = 8.
Step 8: Conclude that the value of A · B is 8.

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