## Find the acute angle between the lines

## (x - 4)/3 = (y + 3)/4 = (z + 1)/5 and (x - 1)/4 = (y + 1)/(-3) = (z + 10)/5

Last updated at Oct. 18, 2019 by Teachoo

Transcript

Question 25 Find the acute angle between the lines (๐ฅ โ 4)/3 = (๐ฆ + 3)/4 = (๐ง + 1)/5 and (๐ฅ โ 1)/4 = (๐ฆ + 1)/(โ3) = (๐ง + 10)/5 Angle between the pair of lines (๐ฅ โ ๐ฅ_1)/๐_1 = (๐ฆ โ ๐ฆ_1)/๐_1 = (๐ง โ ๐ง_1)/๐_1 and (๐ฅ โ ๐ฅ_2)/๐_2 = (๐ฆ โ ๐ฆ_2)/๐_2 = (๐ง โ ๐ง_2)/๐_2 is given by cos ฮธ = |(๐_1 ๐_2 + ๐_1 ๐_2 + ๐_1 ๐_2)/(โ(ใ๐_1ใ^2 + ใ๐_1ใ^2 + ใ๐_1ใ^2 ) โ(ใ๐_2ใ^2 + ใ๐_2ใ^2 + ใ๐_2ใ^2 ))| (๐ โ ๐)/๐ = (๐ + ๐)/๐ = (๐ + ๐)/๐ Comparing with (๐ฅ โ ๐ฅ_1)/๐_1 = (๐ฆ โ ๐ฆ_1)/๐_1 = (๐ง โ ๐ง_1)/๐_1 ๐1 = 3, b1 = 4, c1 = 4 (๐ โ ๐)/๐ = (๐ + ๐)/(โ๐) = (๐ + ๐๐)/๐ Comparing with (๐ฅ โ ๐ฅ_2)/๐_2 = (๐ฆ โ ๐ฆ_2)/๐_2 = (๐ง โ ๐ง_2)/๐_2 ๐2 = 4, ๐2 = โ3, ๐2 = 5 Now, cos ฮธ = |(๐_1 ๐_2 + ๐_1 ๐_2 + ๐_1 ๐_2)/(โ(ใ๐_1ใ^2 + ใ๐_1ใ^2 + ใ๐_1ใ^2 ) โ(ใ๐_2ใ^2 + ใ๐_2ใ^2 + ใ๐_2ใ^2 ))| = |(3 ร 4 + 4 ร (โ3) + 5 ร 5)/(โ(3^2 + 4^2 + 5^2 ) โ(4^2 +(โ3)^2 + 5^2 ))| = |(12 โ 12 + 25)/(โ(9 + 16 + 25) โ(16 + 9 + 25))| = |25/(โ50 โ50)| = |25/50| = |1/2| = 1/2 So, cos ฮธ = 1/2 โด ฮธ = 60ยฐ = ๐ /๐ Therefore, required angle is ๐ /๐ Note: Please write angle in radians and not degree

CBSE Class 12 Sample Paper for 2020 Boards

Paper Summary

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10 Important

Question 11 Important

Question 12

Question 13

Question 14 (OR 1st Question)

Question 14 (OR 2nd Question) Important

Question 15 (OR 1st Question)

Question 15 (OR 2nd Question) Important

Question 16

Question 17 Important

Question 18 (OR 1st Question)

Question 18 (OR 2nd Question)

Question 19

Question 20

Question 21 (OR 1st Question) Important

Question 21 (OR 2nd Question) Important

Question 22

Question 23

Question 24 (OR 1st Question)

Question 24 (OR 2nd Question)

Question 25 You are here

Question 26 Important

Question 27

Question 28 (OR 1st Question) Important

Question 28 (OR 2nd Question)

Question 29

Question 30 Important

Question 31 (OR 1st Question) Important

Question 31 (OR 2nd Question)

Question 32 Important

Question 33 (OR 1st Question) Important

Question 33 (OR 2nd Question) Important

Question 34

Question 35 (OR 1st Question) Important

Question 35 (OR 2nd Question) Important

Question 36 Important

Class 12

Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.