If the vector A = (1, 2) and B = (2, 1), what is the angle between them?
Practice Questions
1 question
Q1
If the vector A = (1, 2) and B = (2, 1), what is the angle between them?
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90 degrees
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180 degrees
Cosine of angle = (A · B) / (|A| |B|) = (1*2 + 2*1) / (√5 * √5) = 4/5, angle = cos^(-1)(4/5).
Questions & Step-by-step Solutions
1 item
Q
Q: If the vector A = (1, 2) and B = (2, 1), what is the angle between them?
Solution: Cosine of angle = (A · B) / (|A| |B|) = (1*2 + 2*1) / (√5 * √5) = 4/5, angle = cos^(-1)(4/5).
Steps: 6
Step 1: Identify the vectors A and B. A = (1, 2) and B = (2, 1).
Step 2: Calculate the dot product of A and B. This is done by multiplying the corresponding components and adding them: A · B = (1 * 2) + (2 * 1) = 2 + 2 = 4.
Step 3: Calculate the magnitude (length) of vector A. |A| = √(1^2 + 2^2) = √(1 + 4) = √5.
Step 4: Calculate the magnitude (length) of vector B. |B| = √(2^2 + 1^2) = √(4 + 1) = √5.
Step 5: Use the formula for the cosine of the angle between two vectors: Cosine of angle = (A · B) / (|A| * |B|). Substitute the values: Cosine of angle = 4 / (√5 * √5) = 4 / 5.
Step 6: Find the angle by taking the inverse cosine: angle = cos^(-1)(4/5).
