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Planes are drawn through the points (5, 0, 2) and (3, -2, 5) parallel to the coordinate planes. Find the lengths of the edges of the rectangular parallelepiped so formed |
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Answer» Given: Points are (5, 0, 2) and (3, -2, 5) To find: lengths of the edges of the parallelepiped formed For point (5, 0, 2) x1 = 5, y1 = 0 and z1 = 2 For point (3, -2, 5) x2 = 3, y2 = -2 and z2 = 5 Plane parallel to coordinate planes of x1 and x2 is yz-plane Plane parallel to coordinate planes of y1 and y2 is xz-plane Plane parallel to coordinate planes of z1 and z2 is xy-plane Distance between planes x1 = 5 and x2 = 3 is 5 – 3 = 2 Distance between planes x1 = 0 and y2 = -2 is 0 – (-2) = 0 + 2 = 2 Distance between planes z1 = 2 and z2 = 5 is 5 – 2 = 3 Hence, edges of parallelepiped is 2, 2, 3 |
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