MHR • Calculus and Vectors 12 Solutions 574 Chapter 6 Section 2 ...

Chapter 6 Section 2 Question 3 Page 325
Answers may vary. For example:
a) The shortest vector is w !" !" " "
; w = u ! v
!!!" !!!" !!!" !!!"
b) The shortest vector is AB ; AB=AC ! BC
c) The shortest vector is RQ
!!!" !!!" !!!" !!!"
; RQ = PQ ! PR
d) The shortest vector is e ! ! ! "!
; e = v ! f
Chapter 6 Section 2 Question 4 Page 325
!!!"
a) AB
!!!"
b) BD
!!!"
c) AC
!!!"
d) AC
!!!"
e) BC
!!!"
!!!"
f) AB ! DB
(parallelogram method)
(parallelogram method)
!!!"
= AB
!!!"
+ BD
!!!"
= AD
!!!"
!!!"
!!!"
!!!"
!!!"
!!!"
g) AB ! CB ! DC = AB + BC + CD
!!!"
= AD
h) The vectors form a triangle.
!!!"
!!!
" !!!"
!!!"
!!!"
!!!"
AE ! EB ! BC = AE + BE + CB
!!!"
!!!"
!!!"
= AE + ED + DA
"
= 0
Chapter 6 Section 2 Question 5 Page 326
Since the hexagon is regular, all sides are equal and all interior angles are equal. Consequently opposite
sides are equal and parallel. Also, the interior triangles formed with the centre are equilateral triangles.
!!!"
!!!"
!!!"
AB = AO + OB
!!!"
!!!"
= !OA + OB
!!!"
!!!"
= OB ! OA
" "
= b ! a
MHR • Calculus and Vectors 12 Solutions 575