Porisma

A hint to get started

Apply the section formula and preserve vertex order

The position vectors of vertices AA, BB and CC, relative to the origin OO, are −3i+4k-3\mathbf i+4\mathbf k, −2i+4j−3k-2\mathbf i+4\mathbf j-3\mathbf k and 11i−4j−9k11\mathbf i-4\mathbf j-9\mathbf k respectively.

(i) Find a unit vector parallel to OA→\overrightarrow{OA}.

(ii) A point PP divides ACAC in the ratio 1:31:3. Find the position vector of PP.

(iii) Show that the points OO, BB and PP are collinear.

(iv) OBDCOBDC forms a parallelogram. Find the position vector of DD.

[2010/RVHS/Promo/6]

CJC · Discussion · Question 3

Write the vertices around the parallelogram in the stated order before choosing an addition formula.

Read the worked solution