
Ex 11.2
Ex 11.2, 2
Ex 11.2, 3 Important You are here
Ex 11.2, 4
Ex 11.2, 5 Important
Ex 11.2, 6
Ex 11.2, 7 Important
Ex 11.2, 8
Ex 11.2, 9 Important
Ex 11.2, 10 (i) Important Deleted for CBSE Board 2022 Exams
Ex 11.2, 10 (ii)
Ex 11.2, 11 (i) Important Deleted for CBSE Board 2022 Exams
Ex 11.2, 11 (ii)
Ex 11.2, 12 Important
Ex 11.2, 13
Ex 11.2, 14 Important
Ex 11.2, 15 Important
Ex 11.2, 16
Ex 11.2, 17 Important
Last updated at Feb. 1, 2020 by Teachoo
Ex 11.2, 3 Show that the line through the points (4, 7, 8), (2, 3, 4) is parallel to the line through the points (–1, –2, 1), (1, 2, 5).Two lines having direction ratios 𝑎1, b1, c1 and 𝑎2, b2, c2 are parallel if 𝒂𝟏/𝒂𝟐 = 𝒃𝟏/𝒃𝟐 = 𝒄𝟏/𝒄𝟐 Also, a line passing through (x1, y1, z1) and (x2, y2, z2) has the direction ratios (x2 − x1), (y2 − y1), (z2 − z1) A (4, 7, 8), B (2, 3, 4) Direction ratios = 2 − 4, 3 − 7, 4 − 8 = −2, −4, −4 ∴ 𝒂𝟏 = −2, 𝒃𝟏 = −4, 𝒄𝟏 = −4 C (−1, −2, 1), D (1, 2, 5) Direction ratios = 1 − (−1), 2 − (−2), 5 − 1 = 2, 4, 4 ∴ 𝒂𝟐 = 2, 𝒃𝟐 = 4, 𝒄𝟐 = 4 Now, 𝑎1/𝑎2 = (−2)/2 = –1 𝑏1/𝑏2 = (−4)/4 = –1 𝑐1/𝑐2 = (−4)/4 = –1 Since 𝑎1/𝑎2 = 𝑏1/𝑏2 = 𝑐1/𝑐2 = −1 Therefore, the given lines are parallel.