Calculate the distance from the point (1, 2, 3) to the origin (0, 0, 0). (2021)

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Question: Calculate the distance from the point (1, 2, 3) to the origin (0, 0, 0). (2021)

Options:

Correct Answer: √14

Exam Year: 2021

Solution:

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

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)

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.

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].