Vector Geometry - 3
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Vector Geometry Name :
Class :
Date : Mark :
→
→
Express the following vectors in terms of z and k. →
→
b) RP
→
c) QR
%
[1]
1) Triangle PQR is shown below where PQ = z and PR = k.
a) PQ
/15
→
d) RQ
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
→
→
[1]
2) OABC is a parallelogram where OA = r and OC = p.
Express the following vectors in terms of r and p. →
a) AB
→
→
b) BC
c) OB
→
→
d) AC
→
[1]
3) ABCD is a rectangle where AB = a and BC = b.
Express the following vectors in terms of a and b. →
a) AD
→
b) AC
→
c) CD
→
d) BD
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
→
→
→
→
[1]
4) ABCD is a trapezium where AB = b, BC = c and AD = 2 BC.
Express the following vectors in terms of c and b. →
a) AC
→
→
b) DB
→
c) CD
→
d) DC
→
[1]
5) ABCDEF is a regular hexagon where OA = r and OB = q.
Express the following vectors in terms of r and q. →
a) AB
→
b) DB
→
c) OC
→
d) FD
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
→
→
[1]
6) Triangle PQR is shown below where PQ = k, PR = w M is the mid-point of QR.
Express the following vectors in terms of k and w. →
→
a) QR
→
b) QM
→
c) PM
→
[1]
7) OABC is a parallelogram where OA = w and OC = x.
Express the following vectors in terms of w and x. →
a) OC
→
b) AC
→
c) BO
→
d) AD
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
→
→
8) ABCD is a rectangle where AB = a, BC = y and M is the mid-point of AD.
[1]
Express the following vectors in terms of a and y. →
→
→
a) AM
b) BM
c) MC
9) ABCD is a trapezium with BC parallel to AD. M is the midpoint of AD and N is the midpoint of BC. →
→
→
[1]
→
Given that AB = 2z, BC = 2b and AD = 6b, express MN in terms of b and z.
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
→ → 10) ABCDEF is a regular hexagon where OA = 6x, OB = 6z and M is the midpoint of BC. [1]
Express the following vectors in terms of x and z. →
→
a) AB
→
b) EF
→
c) EM
→
[1]
11) OPQ is a triangle where OP = k, OQ = c R is the point on QR for which PR:RQ = 1:2.
Express the following vectors in terms of k and c. →
a) QP
→
b) OR
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
→
→
12) OABC is a parallelogram where OA = 6p and OC = 6y.
[1]
1
D is the point on AC for which AD = 3AC.
→
Express OD in terms of p and y.
→
→
13) ABCD is a rectangle where AB = x, BC = a. R is the point on AD for which AR:AD = 2:3.
→
Express BR in terms of x and a.
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
[1]
14) ABCD is a trapezium with BC parallel to AD and AD = 2BC. R is the point on AD for which AR:RD = 3:1. →
→
[1]
→
Given that AB = x and BC = w, express RC in terms of x and w.
→
→
15) ABCDEF is a regular hexagon where AB = x and AC = p.
Express the following vectors in terms of x and p. →
a) BE
→
b) CE
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
[1]
Solutions for the assessment Vector Geometry →
→
1) a) PQ = z
2) a) AB = p
→
→
b) RP = -k
b) BC = −r
→
→
c) QR = -z + k
c) OB = r + p
→
→
d) RQ = z-k
d) AC = p − r
→
→
3) a) AD = b
4) a) AC = b + c
→
→
b) AC = a + b
b) DB = b − 2c →
→
c) CD = c − b
c) CD = −a
→
→
d) DC = b − c
d) BD = b − a
→
5) a) AB = q − r
→
→
6) a) QR = w − k
→
b) QM =
→
c) PM =
b) DB = r + q c) OC = q − r d) FD = q − 2r
→
w
→
2 w
→
b) AC = x − w →
c) BO = −w − x →
1 2
y
8) a) AM =
→
d) AD =
k
+2
2
→
7) a) OC = x
1
x− 2w
→
y
→
2 y
b) BM = c) MC =
2
k
−2
2
−a +a
→
10) a) AB = 6z − 6x →
9) MN = 2z − 2b
→
b) EF = 6x →
c) EM = 12z − 3x
→
11) a) QP = k − c →
b) OR =
→
13) BR =
2k 3
2
c
+3
a−x 3
→
12) OD = 4p + 2y
→
14) RC = x −
w 2
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
→
15) a) BE = 2p − 4x →
b) CE = p − 3x
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
Class :
Date : Mark :
→
→
Express the following vectors in terms of z and k. →
→
b) RP
→
c) QR
%
[1]
1) Triangle PQR is shown below where PQ = z and PR = k.
a) PQ
/15
→
d) RQ
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
→
→
[1]
2) OABC is a parallelogram where OA = r and OC = p.
Express the following vectors in terms of r and p. →
a) AB
→
→
b) BC
c) OB
→
→
d) AC
→
[1]
3) ABCD is a rectangle where AB = a and BC = b.
Express the following vectors in terms of a and b. →
a) AD
→
b) AC
→
c) CD
→
d) BD
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
→
→
→
→
[1]
4) ABCD is a trapezium where AB = b, BC = c and AD = 2 BC.
Express the following vectors in terms of c and b. →
a) AC
→
→
b) DB
→
c) CD
→
d) DC
→
[1]
5) ABCDEF is a regular hexagon where OA = r and OB = q.
Express the following vectors in terms of r and q. →
a) AB
→
b) DB
→
c) OC
→
d) FD
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
→
→
[1]
6) Triangle PQR is shown below where PQ = k, PR = w M is the mid-point of QR.
Express the following vectors in terms of k and w. →
→
a) QR
→
b) QM
→
c) PM
→
[1]
7) OABC is a parallelogram where OA = w and OC = x.
Express the following vectors in terms of w and x. →
a) OC
→
b) AC
→
c) BO
→
d) AD
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
→
→
8) ABCD is a rectangle where AB = a, BC = y and M is the mid-point of AD.
[1]
Express the following vectors in terms of a and y. →
→
→
a) AM
b) BM
c) MC
9) ABCD is a trapezium with BC parallel to AD. M is the midpoint of AD and N is the midpoint of BC. →
→
→
[1]
→
Given that AB = 2z, BC = 2b and AD = 6b, express MN in terms of b and z.
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
→ → 10) ABCDEF is a regular hexagon where OA = 6x, OB = 6z and M is the midpoint of BC. [1]
Express the following vectors in terms of x and z. →
→
a) AB
→
b) EF
→
c) EM
→
[1]
11) OPQ is a triangle where OP = k, OQ = c R is the point on QR for which PR:RQ = 1:2.
Express the following vectors in terms of k and c. →
a) QP
→
b) OR
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
→
→
12) OABC is a parallelogram where OA = 6p and OC = 6y.
[1]
1
D is the point on AC for which AD = 3AC.
→
Express OD in terms of p and y.
→
→
13) ABCD is a rectangle where AB = x, BC = a. R is the point on AD for which AR:AD = 2:3.
→
Express BR in terms of x and a.
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
[1]
14) ABCD is a trapezium with BC parallel to AD and AD = 2BC. R is the point on AD for which AR:RD = 3:1. →
→
[1]
→
Given that AB = x and BC = w, express RC in terms of x and w.
→
→
15) ABCDEF is a regular hexagon where AB = x and AC = p.
Express the following vectors in terms of x and p. →
a) BE
→
b) CE
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
[1]
Solutions for the assessment Vector Geometry →
→
1) a) PQ = z
2) a) AB = p
→
→
b) RP = -k
b) BC = −r
→
→
c) QR = -z + k
c) OB = r + p
→
→
d) RQ = z-k
d) AC = p − r
→
→
3) a) AD = b
4) a) AC = b + c
→
→
b) AC = a + b
b) DB = b − 2c →
→
c) CD = c − b
c) CD = −a
→
→
d) DC = b − c
d) BD = b − a
→
5) a) AB = q − r
→
→
6) a) QR = w − k
→
b) QM =
→
c) PM =
b) DB = r + q c) OC = q − r d) FD = q − 2r
→
w
→
2 w
→
b) AC = x − w →
c) BO = −w − x →
1 2
y
8) a) AM =
→
d) AD =
k
+2
2
→
7) a) OC = x
1
x− 2w
→
y
→
2 y
b) BM = c) MC =
2
k
−2
2
−a +a
→
10) a) AB = 6z − 6x →
9) MN = 2z − 2b
→
b) EF = 6x →
c) EM = 12z − 3x
→
11) a) QP = k − c →
b) OR =
→
13) BR =
2k 3
2
c
+3
a−x 3
→
12) OD = 4p + 2y
→
14) RC = x −
w 2
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
→
15) a) BE = 2p − 4x →
b) CE = p − 3x
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
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