If A = (1, 0) and B = (0, 1), what is the angle between them?

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Question: If A = (1, 0) and B = (0, 1), what is the angle between them?

Options:

Correct Answer: 90 degrees

Solution:

Angle = cos⁻¹((A·B) / (|A||B|)) = cos⁻¹(0) = 90 degrees

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?

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.

Dot Product – The dot product of two vectors is calculated as the sum of the products of their corresponding components.
Magnitude of Vectors – The magnitude of a vector is calculated using the formula |A| = √(x² + y²) for a vector A = (x, y).
Angle Between Vectors – The angle between two vectors can be found using the formula cos(θ) = (A·B) / (|A||B|).