Calculate the distance from the point P(1, 2, 3) to the origin O(0, 0, 0). (2023

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Question: Calculate the distance from the point P(1, 2, 3) to the origin O(0, 0, 0). (2023)

Options:

Correct Answer: √14

Solution:

Distance = √[(1-0)² + (2-0)² + (3-0)²] = √[1 + 4 + 9] = √14.

Calculate the distance from the point P(1, 2, 3) to the origin O(0, 0, 0). (2023)

Calculate the distance from the point P(1, 2, 3) to the origin O(0, 0, 0). (2023)

Step 1: Identify the coordinates of point P, which are (1, 2, 3).
Step 2: Identify the coordinates of the origin O, which are (0, 0, 0).
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 = √[(1 - 0)² + (2 - 0)² + (3 - 0)²].
Step 5: Calculate each squared difference: (1 - 0)² = 1, (2 - 0)² = 4, (3 - 0)² = 9.
Step 6: Add the squared differences together: 1 + 4 + 9 = 14.
Step 7: Take the square root of the sum: Distance = √14.

Distance Formula in 3D – The distance between two points in three-dimensional space is calculated using the formula √[(x2 - x1)² + (y2 - y1)² + (z2 - z1)²].