Slide7.JPG

Slide8.JPG
Slide9.JPG

Go Ad-free

Transcript

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 Thus, the direction ratios are proportional Therefore, the given lines are parallel.

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo