Finding the Diagonal of a Box?

📌 CONCEPT: In Three Dimensional Geometry, we can find the diagonal of a box using the concept of distance between two points in a 3D space.

📐 RULE / FORMULA: The formula to find the distance between two points in 3D space is √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2).

💡 WORKED EXAMPLE: Let's consider a box with dimensions 3 cm x 4 cm x 5 cm. To find the length of the diagonal of each half, we can cut the box along a plane passing through its centre and perpendicular to its length. The coordinates of the corners of the box are (0, 0, 0), (3, 0, 0), (0, 4, 0), and (0, 0, 5). The diagonal of each half is the distance between the points (1.5, 2, 2.5) and (1.5, 0, 0).

⚠️ COMMON MISTAKE: Students often forget to use the correct coordinates or the correct formula to find the diagonal of the box.