If A = i + 2j + 3k and B = 4i + 5j + 6k, what is A - B? (2023)

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Question: If A = i + 2j + 3k and B = 4i + 5j + 6k, what is A - B? (2023)

Options:

Correct Answer: -3i - 3j - 3k

Solution:

A - B = (1 - 4)i + (2 - 5)j + (3 - 6)k = -3i - 3j - 3k.

If A = i + 2j + 3k and B = 4i + 5j + 6k, what is A - B? (2023)

If A = i + 2j + 3k and B = 4i + 5j + 6k, what is A - B? (2023)

Step 1: Identify the components of vector A. A = i + 2j + 3k means A has components: 1 (for i), 2 (for j), and 3 (for k).
Step 2: Identify the components of vector B. B = 4i + 5j + 6k means B has components: 4 (for i), 5 (for j), and 6 (for k).
Step 3: To find A - B, subtract the components of B from the components of A.
Step 4: For the i component: 1 (from A) - 4 (from B) = 1 - 4 = -3.
Step 5: For the j component: 2 (from A) - 5 (from B) = 2 - 5 = -3.
Step 6: For the k component: 3 (from A) - 6 (from B) = 3 - 6 = -3.
Step 7: Combine the results from steps 4, 5, and 6 to write the final answer: A - B = -3i - 3j - 3k.

Vector Subtraction – The question tests the ability to perform vector subtraction by subtracting corresponding components of two vectors.