angle between line and planes_2008

7/29/2019 Angle Between Line and Planes_2008

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Name : __________________________________________ Form : 5 _______

1 Calculate the angle between plane HEL and plane HJKL

2. Calculate the angle between plane LCD with plane HJKL

1

L

MN

K

J

E

10

8

L

H

K

J

10

8

4

CDD

H

6

AB

CD

A B


2/16

Questions Base On SPM Format

1. Diagram 1 shows a pyramid with a

rectangular base PQRS. V is vertically

above P.

Calculate the angle between the line VR

and the plane PQRS.

2. Diagram 2 shows a cuboid with horizontal

base KLMN.

Calculate the angle between the line SL and the

base NKLM.

3. Diagram 3 shows a cuboid.

ACBDEFGH. Given EH = FG = 8 cm.

Calculate the angle between the plane EHD

and the plane FEHG.

4. Diagram 4 shows a right prism with a

horizontal plane ABCD. It is a uniform prism

and its cross section is an isosceles triangle of

sides 4 cm. The thickness of the prism, EA = 4

cm.

Calculate the angle between the plane ABH and

the plane ABE.

2

DIAGRAM 1

DIAGRAM 2

DIAGRAM 3

A B

C

H

E D

DIAGRAM 4

KL

MN

RS

P Q

12 cm

4 cm

5 cm

P Q

RS

V

8 cm

6 cm

11 cm

F E

HB

CD

A

G

7 cm

5 cm

6 cm

4 cm4


3/16

5) Diagram 5 shows a pyramid with the

horizontal plane, TRS. The rectangle PQRS

is vertical plane.

Calculate the angle between the plane PTS

and the plane TQR.

6) Diagram 6 shows a cuboid. Z is the

midpoint of TW .

Calculate the angle between plane YVZ and the

horizontal plane XYVW.

7) Diagram 7 shows a right prism with

base the rectangular plane ABCD. Right

triangle BCF is the uniform cross-section of

the prism. The rectangular surface DCFE is

vertical while the rectangular surface BAEF

is inclined.

Calculate the angle between the plane DB

and plane EDCF.

8) Diagram 8 shows a pyramid REFGH. The

base EFGH is a horizontal rectangle. R is the

midpoint of HG. The apex R is 9 cm vertically

above the point S.

Calculate the angle between line ER and the

plane EFGH.

3

YV

WX

TS

R U

10 cm

6 cm

4 cm4

Z

DIAGRAM 6

T

R

S

QP

12 cm

13 cm

10 cm

DIAGRAM 5

B

DIAGRAM 7DIAGRAM 8

EF

GH

R

5 cm

24 cm

S

A

CD

FE

8 cm

6 cm

6 cm


4/16

9) Diagram 9 shows a cuboid. P is the

midpoint of line RQ.

Calculate the angle between the plane LQY

and the plane MQRN.

10) Diagram 10 shows a right prism. Right

angled triangle SUT is the uniform cross-

section of the prism.

Calvulate the angle between the plane PSR and

the plane PUTR..

11) Diagram 11 shows a prism . The base

PQRS is a horizontal rectangle . X is themidpoint of SR.

Calculate the angle between line PX and

the plane SRML.

12) Diagram 12 shows a right prism with

rectangle base EFGH. EFPQ and GHPQ arerectangle.

Calculate the angle between line LQ and the

base EFGH.

4

DIAGRAM 9 cm

LMM

QP

RS

KNN

Y

10 cm

6 cm

12 cm

U

Q

ST

P

R

5 cm12 cm

20 cm

DIAGRAM 10

PQ

RS

ML

X

12 cm

8 cm

5 cm

DIAGRAM 11 cm

F

G

E

P

H

QQ

MM

L

6 cm

5 cm

12 cm

DIAGRAM 12 cmD


5/16

Name : __________________________________________ Form : 5 _______

a) Name the angle between the two planes.

Example 1: Plane EFGH and

plane GHDA

Angle :

DHE and AGF

1. a) Plane KLSP and plane

JKLM

b) Plane PSWV and plane

VUXW

Example 2 : Plane PQLK andplane SRLK

Angle :

QLR and PKS

2. a) Plane ABCD and planeADEF

b) Plane URST and planeXRSY

Example 3 : Plane TRQ and

plane SRQP

Angle : TRS

3. a) Plane ABCD and plane

ABV

b) Plane PQSR and plane

PQK

c) Plane JKLM and plane

PKL

d) Plane MHEL and plane

NHE

e) Plane ABCD and plane

BCE

5

AB

CD

V

J K

Q

M

RS

P

L

P Q

RS

X

W

V

U

GH

EF

DA

B C

BA

F

E

D C

R S

UT

YX

PQ

RS

LK

P

Q

RS

LK

T

RS

QP

J K

Q

M

RS

P

L

BA

F

E

D C

GH

EF

LK

N MM


6/16

Example 4: Plane DEV and

DEFG

Angle : VMO

4a) Plane GCB and plane

ABCD

b) Plane KLMN and plane

KPN

c) Plane ABE and plane

ABCD

d) Plane RUQ and plane

SRUT

e) Plane SURP and plane

PTR

Exercise 1 : Name the angle between the two planes

a) Plane SRQP and plane QUTR b) Plane JQRM and plane JKLM

c) Plane RSYX and plane URST d) Plane BCF and plane ABCD

6

DE

FG

V

OOM A B

CD

G

OOL

BA

F

E

D C

L

K

R

U

S

P

TQQ

NN

M

J K

Q

M

RS

P

L

R S

UT

YX

BA

F

E

D C

T

LM

NKK

EE

F

P

QQ

WU

R

TT

V

S

P

T

Q

R

U

P

S


7/16

e) Plane GMLF and plane GHEF f) Plane PQA and plane PQRS

C

Exercise 2 : Name the angle between the two planes

a) The diagram shows a pyramid with a

horizontal base DEFG. Name the anglebetween the plane VDE and the plane of

DEFG.

b) The diagram shows a cuboid with a

horizontal base JKLM .Name the anglebetween the plane SRKJ and the plane of

SRLM.

c) The diagram shows a prism. Name the

angle between the plane RSY and the plane

of RSTU.

d) The diagram shows a prism. Name the

angle between the plane ABE and the plane

of ABCD.

7

J K

Q

M

RS

P

L

R S

UT

YX

BA

F

E

D C

Q

P

GH

EF

LK

N M

P Q

RS

X

W

V

U

B

A


8/16

e) The diagram shows a cuboid. Name the

angle between the plane HEK and the plane

of GHEF

f) The diagram shows a prism. Name the

angle between the plane UVWX and the

plane

of

PSWV.

8

GH

EF

LK

NMM


9/16

Name : ________________________________ Form : 5 A1

Date : 30-07-2008 ( 11.10-11.50 12.30)Instruction : Circle the correct answer.

1. Diagram 1 shows a pyramid with a

rectangular base PQRS. V is vertically above

P.

Name the angle between the line VR and the

plane PQRS

A. PRV B. VRS

C. PVQ D. VQS


Name the angle between the line PM and the

plane SRMN.

A. PMK B. PMQ

C. PMR D. PMS

3. In the diagram 3, X and Y are the

midpoints of PW and SV respectively.

The angle between line RX and the plane

RSVU is

A. RXY B. XYR

C. XRY D. XQR

4. Diagram 4 shows a right prism.

Name the angle between line EK and plane

EFJH.

A. EKJ B. EKF

C. HEK D. JEK

9

KL

MN

RS

P Q

P Q

RS

V

DIAGRAM 1DIAGRAM 2

Q P

WS

VU

R TT

X

DIAGRAM 3D

Y

F G

K

H

E J

DIAGRAM 4D


10/16

5. Diagram 5 shows a pyramid .PQRS is a

rectangle.

Name the angle between the line TQ and the

plane PQRS

A. QPT B. QST

C. RST D. SQT


The angle between the line SU and plane

PSWT is

A. USP B. USQ

C. UST D. USW


The angle between plane QPV and the plane

QPWT is

A. VQW B. UQT

C. VPW D. QPV

8. Diagram 8 shows a right prism.

Name the angle between the plane EGKH

and the plane FGKJ.

A. EGF B. EKF

C. HGJ D. GKE

10

TU

VW

RS

P Q

DIAGRAM 5

DIAGRAM 6

Q P

WS

VU

R T

DIAGRAM 7

F G

K

H

E J

DIAGRAM 8

T

RS

QPP


11/16

9. Diagram 9 shows a right prism .

Name the angle between the plane ACS and

the plane SADR.

A. CAS B. SCD

C. ACD D. CAD

10. Diagram 10 shows a right pyramid

MABCD with its square base ABCD .

The angle between the line MC and plane

ABCD is

A. MCD B. MCA

C. AMC D. AMD

11. The diagram 11 shows a right prism on a

horizontal plane. Given that STU is an

equilateral triangle and PV = VR = SW =

WU .

The angle between the plane PRT and the

plane PRUS is

A. PQS B. RQU

C. TQW D. TVW

12. Diagram 12 shows a prism. A and B are

the mid-points of JK and ML, respectively.

JXK and MYL are isosceles triangle.

Name the angle between line AY and the

plane JKLM.

A. YBA B. AYB

C. YAB D. ABY

11

DIAGRAM 11

DIAGRAM 9

Q C

DR

AS

PB

Q

PP

WS

U

R

TT

V

J K

L

Y

XM

DIAGRAM 12D

AA

BB

DIAGRAM 10

A B

CD

M

O


12/16

13. Diagram 13 shows a right prism .

Name the angle between line DM and the

plane ACFD.

A. CDM B. DCM

C. CMD D. DCB

14. Diagram 14 shows a pyramid.

The angle between the plane GHJK and plane

HJL is

A. GHL B. JHL

C. KJL D. KLJ

15. The diagram 15 shows a right prism on a

horizontal plane SRUT. Equilateral triangle

RUQ and STP are the uniform cross-section

of the prism. M and N are the mid-points of

ST and RU, respectively.

The angle between the plane PRN and the

plane RSTU is

A. PRS B. MRP

C. PNM D. NPM

16. Diagram 16 shows a cuboid with base

PQRS . .

Name the angle between the plane WXR and

the plane QRWV.

A. QRX B. RXQ

C. RWX D. SXU

12

DIAGRAM 14DIAGRAM 13

C

DD

MA

B

F

L

JK

HG

R

U

S

P

T

Q

DIAGRAM 15D

NN

M R

Q

U

W

T

S

P

VV

X

DIAGRAM 16D


13/16

17. Diagram 17 shows a cuboid with

rectangular base EFGH .

Name the angle between the plane PSG and

the plane PSHE.

A. SGH B. PGE

C. GSH D. GPE

18. Diagram 18 shows a cuboid on a

horizontal plane EFGH. J is a mid-point of

GH.

The angle between the plane ABGJ and the

plane ABCD is

A. AJE B. AGE

C. GBC D. GAC

19. Diagram 19 shows a prism on a

horizontal plane QRP and vertical rectangular

QRST .

Name the angle between the plane PRS and

the plane QRST is

A. PSQ B. PST

C. PRT D. PRQ

20. Diagram 20 shows a prism with

rectangular base JKLM . LM is normal to

base JKLM .

Name the angle between line NK and base

JKLM.

A. NKM B. NMK

C. NMJ D. NKJ

13

DIAGRAM 17

E

H

R

P

Q

F

G

S

DIAGRAM 20

DIAGRAM 18

A

BC

D

E

F G

HJ

R

T

Q

P

S

DIAGRAM 19

J K

LM

NN


14/16

PAST YEAR SPM QUESTIONS

Nov 2003, Q13

1. Diagram 6 shows a right prism with an isosceles triangle PQR as its horizontal base. M and

N are the mid-point of SU and RQ, respectively.

Name the angle between the plane PQR and the plane PUS.

A. UPT B. NPT

C. PNQ D. MPN

July 2004, Q16

2. Diagram 9 shows a cuboid with PQRS as its horizontal base.

Name the angle between the plane TQR and the plane TUVW.

A. TRW B. TQV

C. WTR D. VTQ

Nov 2004, Q14

3. Diagram 8 shows a cuboid with horizontal base PQRS.

14

T

R Q

USS MM

N

P

PQ

RS

WT

U V

PQ

RS

WT

U V

DIAGRAM 6

DIAGRAM 9


15/16

Name the angle between the line QV and the plane QUR.

A. VUR B. VUQ

C. VQU D. VQR

July 2005, Q14

4. Diagram 6 shows a right pyramid NPQRS with square base PQRS.

The angle between the line NQ and the base PQRS is

A. PQN B. NQS

C. QNS D. QNR

Nov 2005, Q14

5. Diagram 7 shows a right pyramid with a quadrilateral base EFGH.

15

Q R

SP

N

DIAGRAM 8

DIAGRAM 6

E F

GH

V

DIAGRAM 7


16/16

What is the angle between the line VF and the base EFGH ?

A. VFE B. FVH

C. VFH D. FVE

July 2006, Q14

6. Diagram 7 shows a cuboid with a horizontal base TUVW.

The angle between the line PW and the base TUVW is

A. PWV B. PUW

C. PTW D. PWU

Nov 2006, Q14

7. Diagram 7 shows a cuboid with a horizontal base TUVW.

Diagram 7

Name the angle between the plane PQWT and the plane SRWT.

A. QTR B. QWR

C. QTS D. QWS

16

VW

TU

SP

Q R

DIAGRAM 7

angle between line and planes_2008

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