If A = 4i + 5j and B = 1i + 2j, calculate the scalar product A · B. (2022)

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Question: If A = 4i + 5j and B = 1i + 2j, calculate the scalar product A · B. (2022)

Options:

Correct Answer: 14

Exam Year: 2022

Solution:

A · B = (4)(1) + (5)(2) = 4 + 10 = 14.

If A = 4i + 5j and B = 1i + 2j, calculate the scalar product A · B. (2022)

If A = 4i + 5j and B = 1i + 2j, calculate the scalar product A · B. (2022)

Step 1: Identify the components of vector A. A = 4i + 5j means A has a component of 4 in the i direction and 5 in the j direction.
Step 2: Identify the components of vector B. B = 1i + 2j means B has a component of 1 in the i direction and 2 in the j direction.
Step 3: Calculate the product of the i components of A and B. Multiply 4 (from A) by 1 (from B): 4 * 1 = 4.
Step 4: Calculate the product of the j components of A and B. Multiply 5 (from A) by 2 (from B): 5 * 2 = 10.
Step 5: Add the results from Step 3 and Step 4 together. 4 + 10 = 14.
Step 6: The scalar product A · B is 14.

Vector Operations – Understanding how to perform operations on vectors, specifically the scalar (dot) product.
Component-wise Multiplication – Applying the formula for the scalar product by multiplying corresponding components of the vectors.