What is the angle between vectors A = (1, 0, 0) and B = (0, 1, 0)?

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Question: What is the angle between vectors A = (1, 0, 0) and B = (0, 1, 0)?

Options:

Correct Answer: 90 degrees

Solution:

The angle θ = cos⁻¹((A . B) / (|A| |B|)) = cos⁻¹(0) = 90 degrees.

What is the angle between vectors A = (1, 0, 0) and B = (0, 1, 0)?

What is the angle between vectors A = (1, 0, 0) and B = (0, 1, 0)?

Step 1: Identify the vectors A and B. A = (1, 0, 0) and B = (0, 1, 0).
Step 2: Calculate the dot product of A and B. The dot product A . B = (1*0) + (0*1) + (0*0) = 0.
Step 3: Calculate the magnitude of vector A. |A| = √(1^2 + 0^2 + 0^2) = √1 = 1.
Step 4: Calculate the magnitude of vector B. |B| = √(0^2 + 1^2 + 0^2) = √1 = 1.
Step 5: Use the formula for the angle θ: θ = cos⁻¹((A . B) / (|A| |B|)).
Step 6: Substitute the values into the formula: θ = 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 used to find the cosine of the angle between them.
Magnitude of Vectors – The magnitude of a vector is calculated using the square root of the sum of the squares of its components.
Angle Between Vectors – The angle between two vectors can be determined using the inverse cosine of the dot product divided by the product of their magnitudes.