Vector Short Questions (Question 4 & 5)


Question 4:
Diagram below shows a parallelogram ABCD with BED as a straight line.


Given that  AB =7 p ˜ ,  AD =5 q ˜  and DE=3EB, express, in terms of  p ˜  and  q ˜ . (a)  BD (b)  EC
Solution:

(a)
Note: for parallelogram,  AB = DC =7 p ˜ ,  AD = BC =5 q ˜ . BD = BA + AD BD =7 p ˜ +5 q ˜  
(b)
DE =3 EB   EB   DE = 1 3 EB:DE=1:3 EB = 1 4 DB = 1 4 ( BD ) = 1 4 [ ( 7 p ˜ +5 q ˜   ) ]From (a) = 7 4 p ˜ + 5 4 q ˜ EC = EB + BC EC = 7 4 p ˜ + 5 4 q ˜ +5 q ˜ EC = 7 4 p ˜ + 25 4 q ˜


Question 5:

Use the above information to find the values of h and k when r = 2p – 3q.

Solution:
r=2p3q ( h1 ) a ˜ +( h+k ) b ˜ =2( 5 a ˜ 7 b ˜ )3( 2 a ˜ +3 b ˜ ) ( h1 ) a ˜ +( h+k ) b ˜ =10 a ˜ 14 b ˜ +6 a ˜ 9 b ˜ ( h1 ) a ˜ +( h+k ) b ˜ =16 a ˜ 23 b ˜ Comparing vector: h1=16 h=17 h+k=23 17+k=23 k=40