Ex 10.2

Chapter 10 Class 12 Vector Algebra
Serial order wise

Transcript

Ex 10.2, 18 In triangle ABC (Fig 10.18),which of the following is not true (A) (π΄π΅) β + (π΅πΆ) β + (πΆπ΄) β= 0 β (B) (π΄π΅) β + (π΅πΆ) β β (π΄πΆ) β= 0 β (C) (π΄π΅) β + (π΅πΆ) β β (πΆπ΄) β= 0 β (D) (π΄π΅) β β (πΆπ΅) β + (πΆπ΄) β= 0 β In Ξ ABC, (π΄πΆ) β is the resultant of (π΄π΅) β & (π΅πΆ) β (π΄πΆ) β = (π΄π΅) β + (π΅πΆ) β (π΄π΅) β + (π΅πΆ) β = (π΄πΆ) β (π΄π΅) β + (π΅πΆ) β β (π΄πΆ) β = 0 β Checking part (A) (π¨π©) β + (π©πͺ) β + (πͺπ¨) β= π β From (1) (π΄π΅) β + (π΅πΆ) β β (π΄πΆ) β = 0 β (π΄π΅) β + (π΅πΆ) β β (β(πΆπ΄) β) = 0 β (π΄π΅) β + (π΅πΆ) β + (πΆπ΄) β = 0 β Hence, (A) is true. Checking part (B) (π¨π©) β + (π©πͺ) β β (π¨πͺ) β= π β From (1) (π΄π΅) β + (π΅πΆ) β β (π΄πΆ) β = 0 β Hence, (B) is true. Checking part (C) (π¨π©) β + (π©πͺ) β β (πͺπ¨) β= π β From (1) (π΄π΅) β + (π΅πΆ) β β (π΄πΆ) β = 0 β (π΄π΅) β + (π΅πΆ) β β (β(πΆπ΄) β) = 0 β (π΄π΅) β + (π΅πΆ) β + (πΆπ΄) β = 0 β Hence, (C) is not true. Checking part (D) (π¨π©) β β (πͺπ©) β + (πͺπ¨) β= π β From (1) (π΄π΅) β + (π΅πΆ) β β (π΄πΆ) β = 0 β (AB) β β (CB) β + (CA) β = 0 β Hence, (D) is true. Thus, (C) is the correct option