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F4 11 Lines And Planes In 3 Dim

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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.

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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: …………………. 121
ppr maths nbk 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)……….. 122
ppr maths nbk 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 . 123
ppr maths nbk 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)……………………… 124
ppr maths nbk 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. 125
ppr maths nbk 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 126
ppr maths nbk 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 127
ppr maths nbk 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 128
ppr maths nbk 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
ppr maths nbk 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 130

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F4 11 Lines And Planes In 3 Dim

  • 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: …………………. 121
  • 2. ppr maths nbk 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)……….. 122
  • 3. ppr maths nbk 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 . 123
  • 4. ppr maths nbk 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)……………………… 124
  • 5. ppr maths nbk 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. 125
  • 6. ppr maths nbk 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 126
  • 7. ppr maths nbk 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 127
  • 8. ppr maths nbk 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 128
  • 9. ppr maths nbk 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
  • 10. ppr maths nbk 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 130