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If A = (a, b, c) and B = (1, 2, 3), find the value of a if A · B = 10.
If A = (a, b, c) and B = (1, 2, 3), find the value of a if A · B = 10.
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Q1
If A = (a, b, c) and B = (1, 2, 3), find the value of a if A · B = 10.
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A · B = a*1 + b*2 + c*3 = 10. If b = 2 and c = 1, then a + 4 + 3 = 10, so a = 3.
Questions & Step-by-step Solutions
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Q: If A = (a, b, c) and B = (1, 2, 3), find the value of a if A · B = 10.
Solution:
A · B = a*1 + b*2 + c*3 = 10. If b = 2 and c = 1, then a + 4 + 3 = 10, so a = 3.
Steps: 10
Show Steps
Step 1: Identify the vectors A and B. A = (a, b, c) and B = (1, 2, 3).
Step 2: Understand that A · B means to multiply corresponding elements of A and B and then add them together.
Step 3: Write the equation for A · B: A · B = a*1 + b*2 + c*3.
Step 4: Substitute the values of b and c into the equation. We know b = 2 and c = 1.
Step 5: Replace b and c in the equation: A · B = a*1 + 2*2 + 1*3.
Step 6: Calculate the values: A · B = a + 4 + 3.
Step 7: Combine the numbers: A · B = a + 7.
Step 8: Set the equation equal to 10: a + 7 = 10.
Step 9: Solve for a by subtracting 7 from both sides: a = 10 - 7.
Step 10: Calculate the final value: a = 3.
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