What is the distance between the points P(1, 2, 3) and Q(4, 5, 6)?

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Question: What is the distance between the points P(1, 2, 3) and Q(4, 5, 6)?

Options:

Correct Answer: 3√3

Solution:

Distance = √((4-1)² + (5-2)² + (6-3)²) = √(9 + 9 + 9) = 3√3.

What is the distance between the points P(1, 2, 3) and Q(4, 5, 6)?

What is the distance between the points P(1, 2, 3) and Q(4, 5, 6)?

Step 1: Identify the coordinates of point P, which are (1, 2, 3).
Step 2: Identify the coordinates of point Q, which are (4, 5, 6).
Step 3: Use the distance formula for 3D points: Distance = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²).
Step 4: Substitute the coordinates into the formula: Distance = √((4 - 1)² + (5 - 2)² + (6 - 3)²).
Step 5: Calculate each difference: (4 - 1) = 3, (5 - 2) = 3, (6 - 3) = 3.
Step 6: Square each difference: (3)² = 9, (3)² = 9, (3)² = 9.
Step 7: Add the squared differences: 9 + 9 + 9 = 27.
Step 8: Take the square root of the sum: Distance = √(27).
Step 9: Simplify √(27) to 3√3.

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