What is the distance between the points A(1, 2, 3) and B(4, 5, 6)? (2023)

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Question: What is the distance between the points A(1, 2, 3) and B(4, 5, 6)? (2023)

Options:

Correct Answer: 3√2

Solution:

Distance = √[(4-1)² + (5-2)² + (6-3)²] = √[3² + 3² + 3²] = √27 = 3√3.

What is the distance between the points A(1, 2, 3) and B(4, 5, 6)? (2023)

What is the distance between the points A(1, 2, 3) and B(4, 5, 6)? (2023)

Step 1: Identify the coordinates of point A and point B. Point A is (1, 2, 3) and point B is (4, 5, 6).
Step 2: Use the distance formula for 3D points, which is Distance = √[(x2 - x1)² + (y2 - y1)² + (z2 - z1)²].
Step 3: Substitute the coordinates into the formula. Here, x1 = 1, y1 = 2, z1 = 3, x2 = 4, y2 = 5, z2 = 6.
Step 4: Calculate the differences: (x2 - x1) = (4 - 1) = 3, (y2 - y1) = (5 - 2) = 3, (z2 - z1) = (6 - 3) = 3.
Step 5: Square each of the differences: 3² = 9, 3² = 9, 3² = 9.
Step 6: Add the squared differences together: 9 + 9 + 9 = 27.
Step 7: Take the square root of the sum: √27.
Step 8: Simplify √27 to 3√3.

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