1. OAB is a triangle with OA =a and
OB =b. P and Q are the midpoints of
OA and AB, respectively. Express
the vectors in terms of a and b: (a)
PA (b) AB .
Answers: (a) 1 a (b) b - a
2
OAB is a triangle with OA =a and
OB =b. P and Q are the midpoints of
OA and AB, respectively. Express
the vectors in terms of a and b: (a)
AQ (b) PQ.
Answers: (a) 2
1 (b – a) (b) 2
1b
OABC is a rectangle with OA =a and 0B =b.
M is the midpoint of OC, and N is the
midpoint of CB such that CN:NB = 2:1.
2. Express each of the vectors in terms of a and
b: (a) OC (b) ON .
Answers: (a) b – a (b) b - 1a
3
OABC is a rectangle with OA =a and 0B =b.
M is the midpoint of OC, and N is the
midpoint of CB such that CN:NB = 2:1.
Express each of the vectors in terms of a and
b: (a) MO (b) MN .
1 a–2
Answers: (a)2
1b (b) 6
1 a + 2
1b
OABC is a parallelogram with OA =a and
OC =b. S is the point on AB such that
AS:SB=3:1, and T is the point on BC such
that BT:TC = 1:3. Express each of the
vectors in terms of a and b: (a) AC (b) SB .
Answers: (a) b – a (b) 1b
4
3. OABC is a parallelogram with OA =a and
OC =b. S is the point on AB such that
AS:SB=3:1, and T is the point on BC such
that BT:TC = 1:3. Express each of the
vectors in terms of a and b: (a) BT (b) ST .
Answers: (a) -1a (b) 1 (b – a)
4
4
OABC is a trapezoid with OA =a
and OB =b. OA is parallel to, and
twice as long as CB. Express each
of the vectors in terms of a and b:
(a) CB(b) BA .
Answers: (a) 1 a (b) a - b
2
OABC is a rectangle with OB =b
and OB =b. OA is parallel to, and
4. twice as long as CB. Express each
of the vectors in terms of a and b:
(a) CA (b) CO.
Answers: (a) 3 a - b (b) 1 a - b
2
2
OABC is a rectangle with OB =b and OC =a.
R is the point on CB such that CR:RB = 4:1,
and S is the point on AB such that AS:SB =
2:3. Express each of the vectors in terms of a
and b: (a) OA (b) OR .
Answers: (a) b – a (b) 4 b +
1
a
5
5
OABC is a rectangle with OB =b and OC =a.
R is the point on CB such that CR:RB = 4:1,
and S is the point on AB such that AS:SB =
2:3. Express each of the vectors in terms of a
and b: (a) OS (b) RS .
