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Calculate the distance from the point (1, 2, 3) to the origin (0, 0, 0). (2021)
Calculate the distance from the point (1, 2, 3) to the origin (0, 0, 0). (2021)
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Practice Questions
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Q1
Calculate the distance from the point (1, 2, 3) to the origin (0, 0, 0). (2021)
√14
√6
√9
√12
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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 (1, 2, 3) to the origin (0, 0, 0). (2021)
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 the point and the origin. The point is (1, 2, 3) and the origin is (0, 0, 0).
Step 2: Use the distance formula for 3D space, which is Distance = √[(x2 - x1)² + (y2 - y1)² + (z2 - z1)²].
Step 3: Substitute the coordinates into the formula. Here, (x1, y1, z1) = (0, 0, 0) and (x2, y2, z2) = (1, 2, 3).
Step 4: Calculate the differences: (1 - 0) = 1, (2 - 0) = 2, (3 - 0) = 3.
Step 5: Square each of the differences: 1² = 1, 2² = 4, 3² = 9.
Step 6: Add the squared values together: 1 + 4 + 9 = 14.
Step 7: Take the square root of the sum: √14.
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