THE POSITION VECTORS OF POINTS P, Q AND R ARE [1 -1 3], [3 3 1] AND [6 9 -2] RESPECTIVELY. SHOW THAT POINTS P, Q AND R ARE COLLINEAR

​​​​​KCSE 2020 MATHEMATICS ALT A PAPER 2 QUESTION 15

ANSWER

​The diagram below shows a triangle OPQ in which M and N are points on OQ and PQ respectively such that OM = ⅔ OQ and PN = ¼ PQ.  Lines PM and ON meets at X.

(a) Given that OP = P and OQ = q express in term of P and q  the vectors.
(i) PQ

​(ii) PM.                    (2mks)

​(iii) ON.                     (2mks)

​(b) You are further given that OX = KON and PX = hPM.
(i) Express OX in terms of P and q in two different ways.      (2mks)

(ii) Find the value of h and K.   (2mks)

(iii) Find the ratio PX : XM.               (1mk)

The diagram below shows a square based pyramid V vertically above the middle of the base.  PQ = 10cm and VR = 13cm.  M is the midpoint of VR.

​Find
(a) (i) the length of vector PR.                 (2mks)

​(ii) The height of the pyramid.                 (2mks)

(b) (i) the angle between VR and the base PQRS. (2mks)

(ii) The angle between MR and the base PQRS.   (2mks)

(iii) The angle between the planes QVR and PQRS. (2mks)

Worked Solution