4.6.2 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, A B = D C = 7 p ˜ , A D = B C = 5 q ˜ . B D = B A + A D B D = 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 ˜ + 15 4 q ˜


Question 5:

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

Solution:
r = 2 p 3 q ( h 1 ) a ˜ + ( h + k ) b ˜ = 2 ( 5 a ˜ 7 b ˜ ) 3 ( 2 a ˜ + 3 b ˜ ) ( h 1 ) a ˜ + ( h + k ) b ˜ = 10 a ˜ 14 b ˜ + 6 a ˜ 9 b ˜ ( h 1 ) a ˜ + ( h + k ) b ˜ = 16 a ˜ 23 b ˜ Comparing vector: h 1 = 16 h = 17 h + k = 23 17 + k = 23 k = 40

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