A class XII student appearing for a competitive examination was asked to attempt the following questions.

Let a , b  and c  ๐‘e three non zero vectors.

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Question 1
If a   and b  are such that|a + b | = |a – b | then
(a) a ⊥ b โƒ—
(b) a โˆฅ b โƒ—
(c) a = b 
(d) None of these

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Question 2
If a = i ฬ‚ – 2j ฬ‚, b = 2i ฬ‚ + j ฬ‚ + 3k ฬ‚  then evaluate (2a + b) โˆ™ [(a + b) × (a − 2b)]
(a) 0
(b) 4
(c) 3
(d) 2

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Question 3
If a and b are unit vectors and ๐œƒ be the angle between them the, |a โƒ— -b โƒ— | is
(a) sin θ/2
(b) 2 sin θ/2
(c) 2 cos θ/2
(d) cos θ/2

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Question 4
Let a, b  and c be unit vectors such that a โˆ™ b = a โˆ™ c = 0 and angle between b and c โƒ— is π/6 then a =
(a) 2(b × c)
(b) –2 (b × c)
(c) ±2 (b × c)
(d) 2 (b ± c)

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Question 5
The area of the parallelogram formed by a and b as diagonals is
(a) 70
(b) 35
(c) √70/2
(d) √70

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  1. Chapter 10 Class 12 Vector Algebra (Term 2)
  2. Serial order wise

Transcript

Question A class XII student appearing for a competitive examination was asked to attempt the following questions. Let ๐‘Ž โƒ—, ๐‘ โƒ— and ๐‘ โƒ— ๐‘๐‘’ ๐‘กโ„Ž๐‘Ÿ๐‘’๐‘’ non zero vectors. Question 1 If ๐‘Ž โƒ— and ๐‘ โƒ— are such that|๐‘Ž โƒ— + ๐‘ โƒ—| = |๐‘Ž โƒ— โ€“ ๐‘ โƒ—| then (a) ๐‘Ž โƒ— โŠฅ๐‘ โƒ— (b) ๐‘Ž โƒ—โˆฅ๐‘ โƒ— (c) ๐‘Ž โƒ—=๐‘ โƒ— (d) None of these|๐‘Ž โƒ— + ๐‘ โƒ—|2 = |๐‘Ž โƒ— โ€“ ๐‘ โƒ—|2 2.๐‘Ž โƒ— โˆ™ ๐‘ โƒ— = 0, ๐‘Ž โƒ—โŠฅ๐‘ โƒ— Question 2 If ๐‘Ž โƒ— = ๐‘– ฬ‚ โ€“ 2๐‘— ฬ‚, ๐‘ โƒ— = 2๐‘– ฬ‚ + ๐‘— ฬ‚ + 3๐‘˜ ฬ‚ then evaluate (2๐‘Ž โƒ— + ๐‘ โƒ—) โˆ™ [(๐‘Ž โƒ— + ๐‘ โƒ—) ร— (๐‘Ž โƒ— โˆ’ 2๐‘ โƒ—)] (a) 0 (b) 4 (c) 3 (d) 2(a) 0 Question 3 If ๐‘Ž โƒ— and ๐‘ โƒ— are unit vectors and ๐œƒ be the angle between them the, |๐‘Ž โƒ— โˆ’๐‘ โƒ— | is (a) sin ๐œƒ/2 (b) 2 sin ๐œƒ/2 (c) 2 cos ๐œƒ/2 (d) cos ๐œƒ/2(b) 2 sin ๐œƒ/2 Question 4 Let ๐‘Ž โƒ—, ๐‘ โƒ— and ๐‘ โƒ— be unit vectors such that ๐‘Ž โƒ— โˆ™ ๐‘ โƒ— = ๐‘Ž โƒ— โˆ™ ๐‘ โƒ— = 0 and angle between ๐‘ โƒ— and ๐‘ โƒ— is ๐œ‹/6 then ๐‘Ž โƒ— = (a) 2(๐‘ โƒ— ร— ๐‘ โƒ— ) (b) โ€“2 (๐‘ โƒ— ร— ๐‘ โƒ— ) (c) ยฑ2 (๐‘ โƒ— ร— ๐‘ โƒ— ) (d) 2 (๐‘ โƒ—ยฑ๐‘ โƒ— )(c) ยฑ2 (๐‘ โƒ—ร—๐‘ โƒ— ) Question 5 The area of the parallelogram formed by ๐‘Ž โƒ— and ๐‘ โƒ— as diagonals is (a) 70 (b) 35 (c) โˆš70/2 (d) โˆš70โˆš70/2 sq. units

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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.