vector geometry - 1...title vector geometry - 1 author barbara kay created date 3/17/2017 4:55:48 pm
TRANSCRIPT
1
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
Vector Geometry Name : Class : Date :
Mark : /15 %
1) Triangle PQR is shown below where PQ→
= b and PR→
= a.
Express the following vectors in terms of b and a.
a) PQ→
b) RP
→
c) QR→
d) RQ
→
[1]
2) OABC is a parallelogram where OA→
= p and OC→
= x.
Express the following vectors in terms of p and x.
a) AB→
b) BC
→
c) OB→
d) AC
→
[1]
2
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
3) ABCD is a rectangle where AB→
= y and BC→
= c.
Express the following vectors in terms of y and c.
a) AD→
b) AC
→
c) CD→
d) BD
→
[1]
4) ABCD is a trapezium where AB→
= c, BC→
= t and AD→
= 2 BC→
.
Express the following vectors in terms of t and c.
a) AC→
b) DB
→
c) CD→
d) DC
→
[1]
3
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
5) ABCDEF is a regular hexagon where OA→
= p and OB→
= z.
Express the following vectors in terms of p and z.
a) AB→
b) DB
→
c) OC→
d) FD
→
6) Triangle PQR is shown below where PQ→
= b, PR→
= z M is the mid-point of QR.
Express the following vectors in terms of b and z.
a) QR→
b) QM
→
c) PM→
[1]
4
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
7) OABC is a parallelogram where OA→
= q and OC→
= p.
Express the following vectors in terms of q and p.
a) OC→
b) AC
→
c) BO→
d) AD
→
[1]
8) ABCD is a rectangle where AB→
= b, BC→
= x and M is the mid-point of AD.
Express the following vectors in terms of b and x.
a) AM→
b) BM
→
c) MC→
[1]
5
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
9) ABCD is a trapezium with BC parallel to AD. M is the midpoint of AD and N is the midpoint of BC.
Given that AB→
= 2a, BC→
= 2x and AD→
= 6x, express MN→
in terms of x and a.
[1]
10) ABCDEF is a regular hexagon where OA→
= 6p, OB→
= 6q and M is the midpoint of BC.
Express the following vectors in terms of p and q.
a) AB→
b) EF
→
c) EM→
[1]
6
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
11) OPQ is a triangle where OP→
= a, OQ→
= k R is the point on QR for which PR:RQ = 1:2.
Express the following vectors in terms of a and k.
a) QP→
b) OR
→
[1]
7
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
12) OABC is a parallelogram where OA→
= 6r and OC→
= 6t. D is the point on AC for which AD = !
!AC.
Express OD
→ in terms of r and t.
[1]
13) ABCD is a rectangle where AB→
= b, BC→
= z. R is the point on AD for which AR:AD = 2:3.
Express BR
→ in terms of b and z.
[1]
8
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
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.
Given that AB→
= x and BC→
= z, express RC→
in terms of x and z.
[1]
15) ABCDEF is a regular hexagon where AB→
= y and AC→
= q.
Express the following vectors in terms of y and q.
a) BE→
b) CE
→
[1]
9
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
Solutions for the assessment Vector Geometry
1) a) PQ→
= b
b) RP→
= -a
c) QR→
= -b + a
d) RQ→
= b-a
2) a) AB→
= x
b) BC→
= −p
c) OB→
= p+ x
d) AC→
= x− p
3) a) AD→
= c
b) AC→
= y+ c
c) CD→
= −y
d) BD→
= c− y
4) a) AC→
= c+ t
b) DB→
= c− 2t
c) CD→
= t− c
d) DC→
= c− t
5) a) AB→
= z− p
b) DB→
= p+ z
c) OC→
= z− p
d) FD→
= z− 2p
6) a) QR→
= z− b
b) QM→
= !!− !
!
c) PM→
= !!+ !
!
7) a) OC→
= p
b) AC→
= p− q
c) BO→
= −q− p
d) AD→
= !!p− !
!q
8) a) AM→
= !!
b) BM→
= !!− b
c) MC→
= !!+ b
9) MN→
= 2a− 2x
10) a) AB→
= 6q− 6p
b) EF→
= 6p
c) EM→
= 12q− 3p
11) a) QP→
= a− k
b) OR→
= !"!+ !
!
12) OD→
= 4r+ 2t
10
Copyright Mathster.com 2016. Licensed to Thornleigh Salesian College, Bolton
13) BR→
= !!z− b
14) RC
→ = x− !
!
15) a) BE→
= 2q− 4y
b) CE→
= q− 3y