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Question 22
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If vector p = i + j + k and q = i – 2j + k, find a vector of magnitude 5√3 units perpendicular to the vector q and coplanar with vectors p and q

Last updated at Dec. 11, 2018 by Teachoo

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Question 22
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If vector p = i + j + k and q = i – 2j + k, find a vector of magnitude 5√3 units perpendicular to the vector q and coplanar with vectors p and q

Transcript

Question 22 If ๐ โ = ๐ ฬ + ๐ ฬ + ๐ ฬ and ๐ โ = ๐ ฬ โ 2๐ ฬ + ๐ ฬ, find a vector of magnitude 5โ3 units perpendicular to the vector ๐ โ and coplanar with vectors ๐ โ and ๐ โ Let ๐ โ be the required vector ๐ โ = a๐ ฬ + b๐ ฬ + c๐ ฬ Now, given that ๐ โ & ๐ โ are perpendicular Therefore, ๐ โ.๐ โ = 0 (a๐ ฬ + b๐ ฬ + c๐ ฬ) . (๐ ฬ โ 2๐ ฬ + ๐ ฬ) = 0 a ร 1 + b ร (โ2) + c ร 1 = 0 a โ 2b + c = 0 Also, given that ๐ โ is coplanar with vectors ๐ โ and ๐ โ Therefore, [๐ โ" " ๐ โ" " ๐ โ ] = 0 Finding [๐ โ" " ๐ โ" " ๐ โ ] [๐ โ" " ๐ โ" " ๐ โ ] = |โ 8(1&1&1@1&โ2&1@๐&๐&๐)| = 1[โ2๐โ๐ ] โ 1[๐โ๐] + 1[๐+2๐] = โ2๐โ๐โ๐+๐+๐+2๐ = โ3๐+3๐ Since [๐ โ" " ๐ โ" " ๐ โ ] = 0 โ3๐+3๐=0 3๐=3๐ ๐=๐ Now, from (1) a โ 2b + c = 0 Putting c = a a โ 2b + a = 0 2a โ 2b = 0 2a = 2b a = b Therefore, a = b = c So, our vector ๐ โ becomes ๐ โ = a๐ ฬ + b๐ ฬ + c๐ ฬ = a๐ ฬ + a๐ ฬ + a๐ ฬ Also, given that magnitude of ๐ โ is 5โ3 units |๐ โ | = 5โ3 โ(๐^2+๐^2+๐^2 ) = 5โ3 โ(ใ3๐ใ^2 ) = 5โ3 โ3 ๐ = 5โ3 ๐ = 5 So, our vector ๐ โ becomes ๐ โ = a๐ ฬ + a๐ ฬ + a๐ ฬ = 5๐ ฬ + 5๐ ฬ + 5๐ ฬ

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

Question 18

Question 19

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Question 21 (Or 1st)

Question 21 (Or 2nd)

Question 22 You are here

Question 23

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

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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.