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

A cable car line runs from a station A(-3, 1, 2) to a station B(7, -4, -3)…

Contributed by StemPy Lab

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

A cable car line runs from a station $A(-3, 1, 2)$ to a station $B(7, -4, -3)$ . All distances are in metres from a reference point on the hilltop, and a negative $z$ means below it. A clamp $P$ sits on the line between the stations so that $AP : PB = 3 : 2$ . A support $Q$ stands on the line beyond $B$ so that $AQ : QB = 3 : 2$ as well. Find the $x$ -coordinate and the $z$ -coordinate of $P$ . Then find the $x$ -coordinate and the $y$ -coordinate of $Q$ .

Need a reminder? The key ideaShow

The point that divides $AB$ internally in the ratio $m : n$ is $\dfrac{mB + nA}{m + n}$ , coordinate by coordinate. For an external division use $\dfrac{mB - nA}{m - n}$ . A coordinate plane such as $x = 0$ divides $AB$ in the ratio $-x_1 : x_2$ .

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.

← All Problems

← Two drones hover at A(6, -2, 10) and B(-4, 8, 2), with distances in metres measured from a pole at…A ski lift line is straight and joins a top station A(2, -3, 4) to a bottom station B(-1, 5, -3)… →

More onVectors and Three-Dimensional Geometry › Introduction to Three-Dimensional Geometry

Discussion (0)

Loading…