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If I = (a, b, c) and J = (2, 2, 2) such that I · J = 12, what is the relationshi
If I = (a, b, c) and J = (2, 2, 2) such that I · J = 12, what is the relationship between a, b, c?
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Practice Questions
1 question
Q1
If I = (a, b, c) and J = (2, 2, 2) such that I · J = 12, what is the relationship between a, b, c?
a + b + c = 6
2a + 2b + 2c = 12
a + b + c = 12
2a + 2b + 2c = 6
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I · J = 2a + 2b + 2c = 12 gives the equation 2a + 2b + 2c = 12.
Questions & Step-by-step Solutions
1 item
Q
Q: If I = (a, b, c) and J = (2, 2, 2) such that I · J = 12, what is the relationship between a, b, c?
Solution:
I · J = 2a + 2b + 2c = 12 gives the equation 2a + 2b + 2c = 12.
Steps: 8
Show Steps
Step 1: Understand that I = (a, b, c) is a vector with components a, b, and c.
Step 2: Understand that J = (2, 2, 2) is another vector with all components equal to 2.
Step 3: The dot product I · J means we multiply corresponding components of I and J and then add them together.
Step 4: Calculate the dot product: I · J = a * 2 + b * 2 + c * 2.
Step 5: This simplifies to 2a + 2b + 2c.
Step 6: We know from the question that I · J = 12, so we set up the equation: 2a + 2b + 2c = 12.
Step 7: To simplify the equation, divide everything by 2: a + b + c = 6.
Step 8: The relationship between a, b, and c is that their sum equals 6.
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