IB Math SL
Name______________________________________
HW – Position Vectors, Scalar Products, Angle Between Vectors
1.
OAB is a triangle with
respectively.
a.
Express each of these vectors in terms of a and b.
i)
PA
iii)
2.
3.
AQ
ii)
AB
iv)
PQ
OABC is a rectangle with OA  a and OB  b. M is the mid-point of OC, and N is the point on
CB such that CN:NB = 2:1. Express each of these vectors in terms of a and b.
a)
OC
b)
ON
c)
MO
d)
MN
Given p =
a)
4.
OA  a and OB  b. P and Q are the mid-points of OA and AB,
pq
  2
 
 3
q=
1
 
1
and
r=

 5
  evaluate each of these scalar products.
  2
b) r  q  p

c) 2 r  p
Given x = 2i – 3j + k, y = 5i + 2j – 7k, z = i – 4j – 2k, evaluate each of these scalar products.
a) z · z
b) x · (y + z)
c) z · (2x – y)
5.
6.
Decide which of these pairs of vectors are perpendicular, which are parallel, and which are neither.
a) 2i + 8j and 4i – j
b) 6i - 8j + 2k and 9i – 12j + 3k
c) 5i – 6j + 2k and 3i + 2j + k
d)
Find the angle between each of these pairs of vectors, giving your answers correct to one decimal
place.
a) 3i – 4j and 12i + 5j
7.
12 
 1 
  and  
 6
  2
  2
 4
 
 
b)  1  and   3 
 3
 3
 
 
a = 4i + 5j, b = xi – 8j and c = i + yj.
a) Find the value of the constant x given that a and b are perpendicular.
b) Find the value of the constant y given that a and c are parallel.
8.
 c 
 1 




Given that  2  c  and  3  are perpendicular vectors, find the value of the constant c.
 3 
4  c



