Porisma

A hint to get started

Combine parallelogram vectors, an internal angle and a nearest point

With respect to origin O, A and C have position vectors 3i+11j+11k3\mathbf i+11\mathbf j+11\mathbf k and 2i−j+10k2\mathbf i-\mathbf j+10\mathbf k, respectively. B is such that OABC is a parallelogram.

(i) Write down the position vector of B.

(ii) Find angle OAB to the nearest degree.

(iii) Find a vector equation of line AB.

D has position vector −i+13j−9k-\mathbf i+13\mathbf j-9\mathbf k.

(iv) Verify that D is on line AB.

(v) Find the position vector of the point on line AB closest to O.

CJC · Lecture · Example 27

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

Read the worked solution