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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)
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Practice Questions
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Q1
Calculate the distance from the point P(1, 2, 3) to the origin O(0, 0, 0). (2023)
3
√14
√6
√9
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Distance = √[(1-0)² + (2-0)² + (3-0)²] = √[1 + 4 + 9] = √14.
Questions & Step-by-step Solutions
1 item
Q
Q: Calculate the distance from the point P(1, 2, 3) to the origin O(0, 0, 0). (2023)
Solution:
Distance = √[(1-0)² + (2-0)² + (3-0)²] = √[1 + 4 + 9] = √14.
Steps: 7
Show Steps
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.
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