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If A = (1, 0) and B = (0, 1), what is the angle between them?
If A = (1, 0) and B = (0, 1), what is the angle between them?
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Practice Questions
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Q1
If A = (1, 0) and B = (0, 1), what is the angle between them?
0 degrees
90 degrees
45 degrees
180 degrees
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Angle = cos⁻¹((A·B) / (|A||B|)) = cos⁻¹(0) = 90 degrees
Questions & Step-by-step Solutions
1 item
Q
Q: If A = (1, 0) and B = (0, 1), what is the angle between them?
Solution:
Angle = cos⁻¹((A·B) / (|A||B|)) = cos⁻¹(0) = 90 degrees
Steps: 7
Show Steps
Step 1: Identify the vectors A and B. A = (1, 0) and B = (0, 1).
Step 2: Calculate the dot product of A and B. The dot product A·B = (1 * 0) + (0 * 1) = 0.
Step 3: Calculate the magnitude (length) of vector A. |A| = √(1^2 + 0^2) = √1 = 1.
Step 4: Calculate the magnitude (length) of vector B. |B| = √(0^2 + 1^2) = √1 = 1.
Step 5: Use the formula for the angle between two vectors: Angle = cos⁻¹((A·B) / (|A||B|)).
Step 6: Substitute the values into the formula: Angle = cos⁻¹(0 / (1 * 1)) = cos⁻¹(0).
Step 7: Find the angle whose cosine is 0. This angle is 90 degrees.
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