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Question 23Β
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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

CBSE Class 12 Sample Paper for 2019 Boards

Paper Summary

Question 1 Important

Question 2

Question 3

Question 4 (Or 1st) Important

Question 4 (Or 2nd)

Question 5

Question 6

Question 7 Important

Question 8 (Or 1st) Important

Question 8 (Or 2nd)

Question 9

Question 10 (Or 1st) Important

Question 10 (Or 2nd)

Question 11 Important

Question 12 (Or 1st)

Question 12 (Or 2nd)

Question 13 (Or 1st) Important

Question 13 (Or 2nd)

Question 14 Important

Question 15

Question 16 (Or 1st)

Question 16 (Or 2nd) Important

Question 17

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Question 19 Important

Question 20 Important

Question 21 (Or 1st)

Question 21 (Or 2nd) Important

Question 22

Question 23 Important You are here

Question 24 (Or 1st)

Question 24 (Or 2nd) Important

Question 25

Question 26 (Or 1st) Important

Question 26 (Or 2nd)

Question 27 (Or 1st) Important

Question 27 (Or 2nd) Important

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Question 29 Important

Class 12

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

Last updated at Sept. 24, 2021 by Teachoo

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Question 23Β
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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

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