This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — here are the vector calculations for question 6: a) Given A = 2i + 6j - 2k and B = i - 2j + 6k. Find A - B. Step 1: Subtract the corresponding components of vector B from vector A. A - B = (2i + 6j - 2k) - (i - 2j + 6k) Step 2: Group the components. A - B = (2-1)i + (6-(-2))j + (-2-6)k Step 3: Perform the subtraction. A - B = (1)i + (6+2)j + (-8)k A - B = i + 8j - 8k b) Given A = 3i - 4j - 6k and B = 2i - 13j + 9k. Find A - B. Step 1: Subtract the corresponding components of vector B from vector A. A - B = (3i - 4j - 6k) - (2i - 13j + 9k) Step 2: Group the components. A - B = (3-2)i + (-4-(-13))j + (-6-9)k Step 3: Perform the subtraction. A - B = (1)i + (-4+13)j + (-15)k A - B = i + 9j - 15k c) Given A = 5i - 15j - 8k and B = 3i + 8j - 3k. Find A + B. Step 1: Add the corresponding components of vector A and vector B. A + B = (5i - 15j - 8k) + (3i + 8j - 3k) Step 2: Group the components. A + B = (5+3)i + (-15+8)j + (-8+(-3))k Step 3: Perform the addition. A + B = (8)i + (-7)j + (-8-3)k A + B = 8i - 7j - 11k d) Given A = 6i + 5j - 11k and B = 3i - 7j + 8k. Find A + B. Step 1: Add the corresponding components of vector A and vector B. A + B = (6i + 5j - 11k) + (3i - 7j + 8k) Step 2: Group the components. A + B = (6+3)i + (5+(-7))j + (-11+8)k Step 3: Perform the addition. A + B = (9)i + (5-7)j + (-3)k A + B = 9i - 2j - 3k What's next?