Porisma

A hint to get started

Build a line by extending and splitting a displacement

The line l passes through P and Q. The position vector of P is p\mathbf p and PQ→=m\overrightarrow{PQ}=\mathbf m.

(a) Express the position vector of Q in terms of p,m.

(b) E lies on PQ produced with PE=3 PQ; F is the midpoint of PQ; G lies on QP produced with PG:PQ=2:1. (i) Mark E,F,G on the diagram. (ii) Express their position vectors in terms of p,m.

(c) What can you conclude about the position vector of any point R on l?

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The source line l passes through P and Q, with origin O below it, position vector OP=p and displacement PQ=m. The positions of E,F,G are to be supplied.
The source line l passes through P and Q, with origin O below it, position vector OP=p and displacement PQ=m. The positions of E,F,G are to be supplied.
The source line l passes through P and Q, with origin O below it, position vector OP=p and displacement PQ=m. The positions of E,F,G are to be supplied.

CJC · Lecture · Exploration Activity

Choose a point on the line and a nonzero direction; keep one parameter consistent across all components.

Read the worked solution