IB Math SL
Test Review – Vectors
1.
Find the magnitude of each of these vectors.
a)
2.
Name_____________________________________________
 6
 
  2
b) 3i + 5j – k
Given point A = (2, -3, -1) and B = (4, -2, -5),
AB.
a.
find the length of
b.
find a unit vector in the direction of
c.
write the equation of the line through point A and B.
AB.
3.
Given that u = -2i + 3j – 3k and v = -5i -2j + 4k, find u · v.
4.
Show that u = -2i + 3j – k and v = -5i -2j + 4k are perpendicular.
(NOTE: It is not enough to just show the dot product is equal to zero. You need to make a
connection.)
5.
Find p and q so that u = -5i + 6j – k and v = 10i + pj + qk are parallel.
6.
Find the angle between u = 3i – 2j + 4k and v = -2i – 4j + k. (In Degrees Please!)
7.
 6    2
  2  3 
   
   
Find the angle in degrees between r =   3   t   2  and r =  5   s  4  .
  8  1 
 1   4
   
   
(NOTE: Indicated which vectors are being used.)
8.
  2  3 
   
The lines represented by r =   3   t   2  and r =
 1   4
   
 6    2
   
 5   s  4  intersect at point T.
  5  4 
   
Find the coordinates of T.
9.
 4
  2
 
 
Given that PQ    3  and PR   8  find QR.
 5
3
 
 
10.
Consider the vectors u = 2i + 3j – k and v = 4i + j – pk.
a)
Given that u is perpendicular to v, find the value of p.
b) Given that q
u =14, find the value of q.