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Class 12 Tuition > Learn Introduction to Three-dimensional Geometry > If a parallelopiped is formed by planes drawn through...
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If a parallelopiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7) parallel to the coordinate planes, then find the length of edges of a parallelopiped and length of the diagonal

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As an experienced tutor registered on UrbanPro, I can confidently guide you through this problem. UrbanPro is an excellent platform for online coaching and tuition, providing top-notch resources and expert guidance. To find the lengths of the edges of the parallelepiped formed by planes drawn through...
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As an experienced tutor registered on UrbanPro, I can confidently guide you through this problem. UrbanPro is an excellent platform for online coaching and tuition, providing top-notch resources and expert guidance. To find the lengths of the edges of the parallelepiped formed by planes drawn through the points (2, 3, 5) and (5, 9, 7) parallel to the coordinate planes, we need to calculate the differences in coordinates between these points. Let's denote the points as A(2, 3, 5) and B(5, 9, 7). The differences in coordinates give us the lengths of the edges of the parallelepiped along the x, y, and z directions. Length of the edges: Along x-axis: |5 - 2| = 3 units Along y-axis: |9 - 3| = 6 units Along z-axis: |7 - 5| = 2 units Now, to find the length of the diagonal of the parallelepiped, we can use the distance formula in three dimensions. Let's denote the diagonal as d. Using the coordinates of points A and B: d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²] Substituting the coordinates: d = √[(5 - 2)² + (9 - 3)² + (7 - 5)²] = √[3² + 6² + 2²] = √(9 + 36 + 4) = √49 = 7 units So, the lengths of the edges of the parallelepiped are 3 units, 6 units, and 2 units along the x, y, and z directions respectively. The length of the diagonal of the parallelepiped is 7 units. If you need further clarification or assistance, feel free to ask! read less
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