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Ex 11.3
Ex 11.3, 1 (b)
Ex 11.3, 1 (c) Important
Ex 11.3, 1 (d) Important
Ex 11.3, 2
Ex 11.3, 3 (a)
Ex 11.3, 3 (b)
Ex 11.3, 3 (c) Important
Ex 11.3, 4 (a) Important
Ex 11.3, 4 (b)
Ex 11.3, 4 (c)
Ex 11.3, 4 (d) Important
Ex 11.3, 5 (a) Important
Ex 11.3, 5 (b)
Ex 11.3, 6 (a) Important
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Ex 11.3, 10 Important
Ex 11.3, 11 Important
Ex 11.3, 12 Important Deleted for CBSE Board 2022 Exams
Ex 11.3, 13 (a) Important Deleted for CBSE Board 2022 Exams
Ex 11.3, 13 (b) Important You are here
Ex 11.3, 13 (c)
Ex 11.3, 13 (d)
Ex 11.3, 13 (e) Deleted for CBSE Board 2022 Exams
Ex 11.3, 14 (a) Important
Ex 11.3, 14 (b)
Ex 11.3, 14 (c)
Ex 11.3, 14 (d) Important
Last updated at Aug. 23, 2021 by Teachoo
Ex 11.3, 13 In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them. (b) 2x + y + 3z β 2 = 0 and x β 2y + 5 = 0 Check parallel Two lines with direction ratios π΄_1, π΅_1, πΆ_1 and π΄_2, π΅_2, πΆ_2 are parallel if π¨_π/π¨_π = π©_π/π©_π = πͺ_π/πͺ_π So, π΄_1/π΄_2 = 2/(β1) = β2, π΅_1/π΅_2 = 1/2 , πΆ_1/πΆ_2 = 3/0 Since, direction ratios are not proportional, the two normal are not parallel. β΄ Given two planes are not parallel. Check perpendicular Two lines with direction ratios π΄_1, π΅_1, πΆ_1 and π΄_2, π΅_2, πΆ_2 are perpendicular if π¨_π π¨_π + π©_π π©_π + πͺ_π πͺ_π = 0 Now, π΄_1 π΄_2 + π΅_1 π΅_2 + πΆ_1 πΆ_2 = (2 Γ β1) + (1 Γ 2) + (3 Γ 0) = β2 + 2 + 0 = 0 Since π΄_1 π΄_2 + π΅_1 π΅_2 + πΆ_1 πΆ_2 = 0 The two normal are perpendicular. Since normal are perpendicular, planes are perpendicular.