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If A = (a, b, c) and B = (1, 2, 3) such that A · B = 0, what is the relation bet
If A = (a, b, c) and B = (1, 2, 3) such that A · B = 0, what is the relation between a, b, and c?
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Practice Questions
1 question
Q1
If A = (a, b, c) and B = (1, 2, 3) such that A · B = 0, what is the relation between a, b, and c?
a + 2b + 3c = 0
a - 2b + 3c = 0
a + b + c = 0
a - b - c = 0
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A · B = a*1 + b*2 + c*3 = 0. Thus, a + 2b + 3c = 0.
Questions & Step-by-step Solutions
1 item
Q
Q: If A = (a, b, c) and B = (1, 2, 3) such that A · B = 0, what is the relation between a, b, and c?
Solution:
A · B = a*1 + b*2 + c*3 = 0. Thus, a + 2b + 3c = 0.
Steps: 6
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 the dot product of A and B.
Step 3: Write the formula for the dot product: A · B = a*1 + b*2 + c*3.
Step 4: Simplify the expression: A · B = a + 2b + 3c.
Step 5: Set the dot product equal to 0, since A · B = 0: a + 2b + 3c = 0.
Step 6: This equation (a + 2b + 3c = 0) shows the relationship between a, b, and c.
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