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A drone flies in a straight line from A(-1, 2, 5) to B(7, -2, 1), with all coordinates in metres…

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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 drone flies in a straight line from $A(-1, 2, 5)$ to $B(7, -2, 1)$ , with all coordinates in metres. A flat wall of a building is the plane $x = 2$ . The drone passes through the wall at a window. Find the ratio $AP : PB$ at the window $P$ , as a decimal. Then find the $y$ -coordinate and the $z$ -coordinate of $P$ .

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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