The document contains 10 problems involving calculating angles between lines and planes in 3-dimensional space. Specifically, it contains: 1) Problems calculating angles between lines and planes in pyramids and cuboids. 2) A diagnostic test with 10 multiple choice questions assessing the ability to name and calculate angles between lines and planes in various 3D shapes. 3) The document provides practice for understanding lines and planes in 3D geometry, particularly as it relates to pyramids, cuboids, and calculating angles between geometric elements in 3-dimensional space.

1. ppr maths nbk
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
10. K
G
H
E F 129

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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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