EasyMathematicsHigh School (11–12)Vectors and Three-Dimensional Geometry › Introduction to Three-Dimensional GeometryNumerical

A room is a cuboid. A corner of the floor is the origin…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A room is a cuboid. A corner of the floor is the origin. The room is $6\ \text{m}$ long along the $x$ -axis, $6\ \text{m}$ wide along the $y$ -axis and $7\ \text{m}$ high. A cable runs from the origin to the opposite corner of the ceiling. Find the length of the cable. Then find the length of the diagonal of the floor, to two decimal places.

Need a reminder? The key ideaShow

A cuboid with edges $a$ , $b$ , $c$ has the diagonal $\sqrt{a^2 + b^2 + c^2}$ . The distance from a point to a line is found by writing the squared distance as a quadratic in $t$ . The plane $x = k$ cuts the segment $AB$ in the ratio $(k - x_1) : (x_2 - k)$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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