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CHAPTER 11 : LINES AND PLANES IN 3-DIMENSION
EXERCISE 1 (PAPER 2)
1. The diagram shows a pyramid with a triangular base LMN
K
3 cm
5 cm
L N
3 cm
M
The apex K is vertically above point L. Calculate
(a) the angle between line KN and the base LMN
(b) the angle between the planes KLM and KLN
Answer: (a)……..……........
(b)……….…….....
2. The digram shows a pyramid with vertex V which is 4 cm vertically above N.
V
A
N B
5 cm
D 12 cm C
The digram shows a pyramid with vertex V which is 4 cm vertically above N.
Calculate the angle between the edge VC and the plane ABCD.
Answer: ………………….
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3. The diagram shows a cuboid.
D C
A B 3 cm
E H
8 cm
F 6 cm G
Calculate
(a) the length of EG
(b) the angle between line DG and the base EFGH
Answer: (a)…………...
(b)…………..
4. The diagram shows a right pyramid with rectangular base PQRS and
VT = 5cm.
V
S
R
T
6 cm
P 8 cm Q
Calculate
(a) the angle between VP and plane PQRS
(b) the angle between plane VQR and plane PQRS
Answer: (a)…………
(b)………..
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5. The diagram shows a cuboid. S and T are the mid points of BF and AE respectively.
H 8 cm G
E F
30 cm
T S
D C
6 cm
A B
Calculate
(a) the length of BT
(b) the angle between line CT and the base ABCD
(c) the angle between the planes BCT and BCGF
Answer: (a)………….
(b)………….
(c) …………
.
6. The diagram shows pyramid with a rectangular base PQRS.
M
S R
8 cm.
P 6 cm. Q
Given that MS = 8 cm. , calculate the angle between the line MQ and the base
PQRS .
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Answer : …………………
7. The diagram shows a cuboid.
D
C
A S 2
B R
P
3 cm. 5 cm.
Q
Calculate the angle between the line DQ and the plane BCRQ.
Answer : …………………….
8. The diagram shows a cuboid.
M P Q
D C
S
6 N
R
A 10 cm.
12 cm. B
M and N are the midpoints of DP and AS respectively.
(a) Name the angle between planes ABM and ABCD.
(b) Calculate the angle between line BM and plane ABRS.
Answer :(a)……….………...........
(b)………………………
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9. The diagram shows a cuboid with a horizontal rectangular base EFGH
A B
D 4 cm.
E C
F
3 cm.
H 8 cm. G
Calculate the angle between;
(a) plane HGB and base EFGH.
(b) line BH and plane ABCD.
Answer : (a) ………………….............
(b)………………………..…
10. The diagram shows a pyramid and right – angled triangle RST is horizontal
P 24 cm. R
7 cm.
Q S
30 cm.
T
(a) Name the angle between planes QST and PRT
(b) Calculate the angle between line PT and plane PQSR.
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Answer : (a) …………………………
(b)…………………………..
CHAPTER 11 : LINES AND PLANES IN 3-DIMENSION
DIAGNOSTIC TEST
1. The diagram shows a cube with a horizontal base ABCD
E H
F
G
D C
A B
Name the angle between line AF and the plane ABE
A. ∠ EAB
B. ∠ EAF
C. ∠ EBA
D. ∠ EBF
2. B C
A D
Q
R
P M
S
The diagram shows a cuboid. Name the angle between line BM and the plane PRQS
A. ∠ BRQ
B. ∠ BMQ
C. ∠ BMR
D. ∠ BMS
W
V
3.
T U
R
S
P Q
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The diagram shows a cuboid. The angle between line SU and plane PSWT is
A. ∠ USP
B. ∠ USQ
C. ∠ UST
D. ∠ USW
4. The diagram shows a right pyramid with a quardrilateral base PQRS.
V
Q
P R
S
What is the angle between the line VQ and the base PQRS?
A. ∠ VQR
B. ∠ VQP
C. ∠ VQS
D. ∠ QVR
5. The diagram shows a cuboid with a horizontal base GHIJ
P Q
R
S
H
I
G J
Name the angle between line QI and the plane JPI
A. ∠ QJP
B. ∠ QPI
C. ∠ QIH
D. ∠ QIP
6. W
T
S
V
P
U
R
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The diagram shows a cuboid. Name the angle between the two planes PSTW
and VSP
A ∠ VPW
B ∠ VSW
C ∠ VSP
D ∠ VPT
7.
E H
K
F G
S
P
R
Q
The diagram shows a cuboid . The angle between the two planes PQKH and GHSR is
A. ∠ PHK
B. ∠ PHS
C. ∠ PHE
D. ∠ QKS
T R
8
P
S
Q
The diagram shows a pyramid with a horizontal triangular base PQR. RSTP is a
vertical plane. The angle between the two planes TPQ and SRQ is
A ∠ PRQ
B ∠ SQR
C ∠ PQS
D ∠ TQS
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9. P R
M
Q
A C
N
B
The diagram shows a right prism with triangle ABC as its uniform cross section. The
angle between the two planes AMN and ABQP is
A ∠ MAN
B ∠ MAQ
C ∠ MAB
D ∠ BAN
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G
H
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The diagram shows a pyramid with a rectangular base EFGH . HK is normal to the
base. The angle between the two plane FGK and EHK is
A. ∠ EKF
B ∠ EKG
C ∠ HKG
D ∠ HGK
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