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|vec A|=5 |bar(B)|=4& angle between bar(A)&bar(B) is 60^(0) then |bar(A)-bar(B)| will be 8. (B) 4 (A) 5 (D) none of these. |
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Answer» (D) NONE of these |⃗A - ⃗B| = √21 Explanation: Given |⃗A| = 5 |⃗B| = 4, θ = 60º Calculation. We know that for any vector ⃗X, ⃗X. ⃗X = |⃗X||⃗X|cos(0) = |⃗X|² Applying this with ⃗A - ⃗B we GET |⃗A - ⃗B|² = (⃗A - ⃗B).(⃗A - ⃗B) = ⃗A.⃗A - ⃗A.⃗B - ⃗B.⃗A + ⃗B.⃗B = |⃗A|² - 2|⃗A||⃗B|cos(θ) + |⃗B|² = 5² - 2*5*4*cos(60º) + 4² = 25 - 2*5*4*(1/2) +16 = 25 + 16 - 20 = 21 or |⃗A - ⃗B| = √21
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