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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

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Last updated at Oct. 1, 2019 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

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Transcript

Question 22 If π β = π Μ + π Μ + π Μ and π β = π Μ β 2π Μ + π Μ, find a vector of magnitude 5β3 units perpendicular to the vector π β and coplanar with vectors π β and π β Let π β be the required vector π β = aπ Μ + bπ Μ + cπ Μ Now, given that π β & π β are perpendicular Therefore, π β.π β = 0 (aπ Μ + bπ Μ + cπ Μ) . (π Μ β 2π Μ + π Μ) = 0 a Γ 1 + b Γ (β2) + c Γ 1 = 0 a β 2b + c = 0 Also, given that π β is coplanar with vectors π β and π β Therefore, [π β" " π β" " π β ] = 0 Finding [π β" " π β" " π β ] [π β" " π β" " π β ] = |β 8(1&1&1@1&β2&1@π&π&π)| = 1[β2πβπ ] β 1[πβπ] + 1[π+2π] = β2πβπβπ+π+π+2π = β3π+3π Since [π β" " π β" " π β ] = 0 β3π+3π=0 3π=3π π=π Now, from (1) a β 2b + c = 0 Putting c = a a β 2b + a = 0 2a β 2b = 0 2a = 2b a = b Therefore, a = b = c So, our vector π β becomes π β = aπ Μ + bπ Μ + cπ Μ = aπ Μ + aπ Μ + aπ Μ Also, given that magnitude of π β is 5β3 units |π β | = 5β3 β(π^2+π^2+π^2 ) = 5β3 β(γ3πγ^2 ) = 5β3 β3 π = 5β3 π = 5 So, our vector π β becomes π β = aπ Μ + aπ Μ + aπ Μ = 5π Μ + 5π Μ + 5π Μ

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

Question 20

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

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.