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If the vector A = (a, b) is perpendicular to B = (b, -a), what is the relationsh
If the vector A = (a, b) is perpendicular to B = (b, -a), what is the relationship between a and b?
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Practice Questions
1 question
Q1
If the vector A = (a, b) is perpendicular to B = (b, -a), what is the relationship between a and b?
a = b
a = -b
a + b = 0
a - b = 0
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Copy
A·B = ab - ab = 0, hence A and B are perpendicular if a = -b.
Questions & Step-by-step Solutions
1 item
Q
Q: If the vector A = (a, b) is perpendicular to B = (b, -a), what is the relationship between a and b?
Solution:
A·B = ab - ab = 0, hence A and B are perpendicular if a = -b.
Steps: 7
Show Steps
Step 1: Understand that two vectors are perpendicular if their dot product is zero.
Step 2: Write down the vectors: A = (a, b) and B = (b, -a).
Step 3: Calculate the dot product of A and B: A·B = a * b + b * (-a).
Step 4: Simplify the dot product: A·B = ab - ab.
Step 5: Notice that ab - ab equals 0, which means A·B = 0.
Step 6: Since the dot product is zero, A and B are perpendicular.
Step 7: From the calculation, we see that the relationship between a and b is that a must equal -b.
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