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#VectorInSpace #Prove #Vector Second Year Mathematic Chapter 7 Complete Exercise 7.2 By Muhammad Atif Firdous In this lecture i am going to discuss ▶ 00:00 Start ▶ 01:27 INTRODUCTION OF VECTOR IN SPACE ▶ 03:17 Right Hand Rule ▶ 04:17 Unique triple of Real Numbers ▶ 05:47 Concept of a vector in space ▶ 07:17 We define addition and scalar multiplication in 𝐑^𝟑 ▶ 08:37 Set of vectors in 𝑹^𝟑 ▶ 11:37 Position Vector ▶ 12:13 Magnitude of a vector ▶ 12:51 Properties of Vectors ▶ 16:11 Another notation for representing vectors in space ▶ 21:31 Distance Between two Points in Space ▶ 24:31 Direction Angles and Direction Cosines of a Vector ▶ 27:15 Prove that 〖𝑪𝒐𝒔〗^𝟐 𝜶+〖𝑪𝒐𝒔〗^𝟐 𝜷+〖𝑪𝒐𝒔〗^𝟐 𝜸=𝟏 ▶ 31:45 Question Number 1 Part ( i ) ▶ 34:05 Question Number 1 Part ( ii ) ▶ 35:39 Question Number 1 Part ( iii ) ▶ 36:49 Question Number 2 Part ( i ) ▶ 38:09 Question Number 2 Part ( ii ) ▶ 38:47 Question Number 2 Part ( iii ) ▶ 40:01 Question Number 3 Part ( i ) ▶ 42:15 Question Number 3 Part ( ii ) ▶ 43:06 Question Number 3 Part ( iii ) ▶ 44:35 Question Number 4 ▶ 46:25 Question Number 5 ▶ 47:55 Question Number 6 ▶ 50:55 Question Number 7 Part ( i ) ▶ 55:55 Question Number 7 Part ( ii ) ▶ 57:55 Question Number 8 ▶ 59:29 Question Number 9 ▶ 01:03:29 Question Number 10 Part ( a ) ▶ 01:06:37 Question Number 10 Part ( b ) ▶ 01:08:45 Question Number 10 Part ( c ) ▶ 01:10:35 Question Number 10 Part ( d ) ▶ 01:12:35 Question Number 11 Part ( i ) ▶ 01:13:13 Question Number 11 Part ( ii ) ▶ 01:14:43 Question Number 11 Part ( iii ) ▶ 01:16:23 Question Number 12 Part ( i ) ▶ 01:18:05 Question Number 12 Part ( ii ) ▶ 01:19:09 Question Number 12 Part ( iii ) Topic Related to all Boards Mathematics Bise Faisalabad BOARD Bise Gujranwala BOARD Bise Sargodha Board Bise Sahiwal Board Bise Dera Ghazi Khan Board Bise Bahawalpur Board Bise Rawalpindi Board Bise Multan Board Bise LAHORE BOARD Fbise Federal Board Punjab Board Follow me on LinkedIn: / muhammad-atif-firdous-53788325 Follow me on Twitter: / muhamma65673226