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Last updated at Aug. 18, 2020 by Teachoo
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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 โ 2 = 0 and x โ 2y + 5 = 0 Check parallel Two lines with direction ratios ๐ด_1, ๐ต_1, ๐ถ_1 and ๐ด_2, ๐ต_2, ๐ถ_2 are parallel if ๐จ_๐/๐จ_๐ = ๐ฉ_๐/๐ฉ_๐ = ๐ช_๐/๐ช_๐ So, ๐ด_1/๐ด_2 = 2/(โ1) = โ2, ๐ต_1/๐ต_2 = 1/2 , ๐ถ_1/๐ถ_2 = 3/0 Since, direction ratios are not proportional, the two normal are not parallel. โด Given two planes are not parallel. Check perpendicular Two lines with direction ratios ๐ด_1, ๐ต_1, ๐ถ_1 and ๐ด_2, ๐ต_2, ๐ถ_2 are perpendicular if ๐จ_๐ ๐จ_๐ + ๐ฉ_๐ ๐ฉ_๐ + ๐ช_๐ ๐ช_๐ = 0 Now, ๐ด_1 ๐ด_2 + ๐ต_1 ๐ต_2 + ๐ถ_1 ๐ถ_2 = (2 ร โ1) + (1 ร 2) + (3 ร 0) = โ2 + 2 + 0 = 0 Since ๐ด_1 ๐ด_2 + ๐ต_1 ๐ต_2 + ๐ถ_1 ๐ถ_2 = 0 The two normal are perpendicular. Since normal are perpendicular, planes are perpendicular.
Ex 11.3
Ex 11.3, 2
Ex 11.3, 3
Ex 11.3, 4 Important
Ex 11.3, 5 Important
Ex 11.3, 6 Important
Ex 11.3, 7
Ex 11.3, 8
Ex 11.3, 9
Ex 11.3, 10 Important
Ex 11.3, 11 Important
Ex 11.3, 12 Important Not in Syllabus - CBSE Exams 2021
Ex 11.3, 13 (a) Important
Ex 11.3, 13 (b) You are here
Ex 11.3, 13 (c)
Ex 11.3, 13 (d)
Ex 11.3, 13 (e)
Ex 11.3, 14 (a) Important
Ex 11.3, 14 (b)
Ex 11.3, 14 (c)
Ex 11.3, 14 (d)
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