Express Vector LN in terms of r and s
In the diagram, LOM is a diameter of the the circle with centre O. N is a point on the circumference of the circle If vector r=ON and vector s=MN, express LN in terms of r and s
I assumed that because r=ON and ON was just the radius that 2r would therefore = LOM, but that would be |r| not r because of direction as well i'm pretty sure. And then I said 2r+s=LM + MN but because r doesn't have a direction in my answer I presume it is wrong. Any help? [] [Diagram]1
$\endgroup$1 Answer
$\begingroup$$$\overrightarrow{LO} = \overrightarrow{OM}$$
because they're the same magnitude and direction.
$$\overrightarrow{OM} = \overrightarrow{ON} + \overrightarrow{NM} = \underline{r} - \underline{s}$$
So
$$\overrightarrow{LO} = \underline{r} - \underline{s}$$
$$\overrightarrow{LN} = \overrightarrow{LO} + \overrightarrow{ON}$$
$$\overrightarrow{LN} = (\underline{r} - \underline{s}) + \underline{r}$$
$$\overrightarrow{LN} = 2\underline{r} - \underline{s}$$
$\endgroup$
