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Question 23
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Find the vector equation of the line joining (1, 2, 3) and (–3, 4, 3) and show that it is perpendicular to the z-axis

Last updated at Dec. 12, 2018 by Teachoo

**
Question 23
**

Find the vector equation of the line joining (1, 2, 3) and (–3, 4, 3) and show that it is perpendicular to the z-axis

Transcript

Question 23 Find the vector equation of the line joining (1, 2, 3) and (β3, 4, 3) and show that it is perpendicular to the z-axis Vector equation of a line passing though two points with position vectors π β and π β is π β = (π ) β + π (π β β π β) Given, Let two points be A (1, 2, 3) & B(β3, 4, 3) A (1, 2, 3) π β = 1π Μ + 2π Μ + 3π Μ B (β3, 4, 3) π β = β3π Μ + 4π Μ + 3π Μ So, π β = (1π Μ + 2π Μ + 3π Μ) + π [("β3" π Μ" + 4" π Μ" + 3" π Μ" " ) β ("1" π Μ" + 2" π Μ" + 3" π Μ)] = (1π Μ + 2π Μ + 3π Μ) + π [(β3β1) π Μ+(4β2) π Μ+(3β3)π Μ ] = (1π Μ + 2π Μ + 3π Μ) + π (β4π Μ + 2π Μ) So, equation of line is π β = (1π Μ + 2π Μ + 3π Μ) + π (β4π Μ + 2π Μ) Also, we have to prove that line is perpendicular to z-axis So, parallel vector of line will be perpendicular to z-axis Theory : Two lines with direction ratios π1, b1, c1 and π2, b2, c2 are perpendicular if π1 π2 + b1b2 + c1 c2 = 0 Finding direction ratios of parallel and z-axis β4π Μ + 2π Μ Direction ratios = β4, 2, 0 β΄ π1 = β4, b1 = 2, c1 = 0 (πΆπ) β = 0π Μ + 0π Μ + 1π Μ Direction ratios = 0, 0, 1 β΄ π2 = 0, b2 = 0, c2 = 1, Now, π1 π2 + b1 b2 + c1 c2 = β4 Γ 0 + 2 Γ 0 + 0 Γ 1 = 0 Since π1 π2 + b1 b2 + c1 c2 = 0 So, parallel vector of line is perpendicular to z-axis Hence proved

CBSE Class 12 Sample Paper for 2019 Boards

Paper Summary

Question 1

Question 2

Question 3

Question 4 (Or 1st)

Question 4 (Or 2nd)

Question 5

Question 6

Question 7

Question 8 (Or 1st)

Question 8 (Or 2nd)

Question 9

Question 10 (Or 1st)

Question 10 (Or 2nd)

Question 11

Question 12 (Or 1st)

Question 12 (Or 2nd)

Question 13 (Or 1st)

Question 13 (Or 2nd)

Question 14

Question 15

Question 16 (Or 1st)

Question 16 (Or 2nd)

Question 17

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Question 19

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Question 21 (Or 1st)

Question 21 (Or 2nd)

Question 22

Question 23 You are here

Question 24 (Or 1st)

Question 24 (Or 2nd)

Question 25

Question 26 (Or 1st)

Question 26 (Or 2nd)

Question 27 (Or 1st)

Question 27 (Or 2nd)

Question 28

Question 29

Class 12

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

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.