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CBSE Class 11-science Answered

A vector a of magnitude 50 is collinear with the vector 6^I-8^J-(15/2)^K making an obtuse angle
with the Z-axis is
 
1)24^i-32^j-30^k       2)-24^i+32^j+30^k
3)24^i+32^j-30^k       4)12^i-16^j-15^k
 
 
 
 
 
 
 
 
Asked by Sunil Soni | 12 Jan, 2016, 11:08: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight b with rightwards arrow on top equals 6 straight i with hat on top minus 8 straight j with hat on top minus 15 over 2 straight k with hat on top unit space vector space along space vector stack space straight b space with rightwards arrow on top is equals fraction numerator stack space straight b space with rightwards arrow on top over denominator open vertical bar stack space straight b space with rightwards arrow on top close vertical bar end fraction equals fraction numerator 6 straight i with hat on top minus 8 straight j with hat on top minus 15 over 2 straight k with hat on top over denominator square root of 6 squared plus 8 squared plus open parentheses begin display style 15 over 2 end style close parentheses squared end root end fraction equals plus-or-minus 2 over 25 open parentheses 6 straight i with hat on top minus 8 straight j with hat on top minus 15 over 2 straight k with hat on top close parentheses straight A space vector space straight m with rightwards arrow on top space of space magnitude space 50 space collinear space with space straight b with rightwards arrow on top space is space stack straight m space with rightwards arrow on top equals 50 cross times open square brackets plus-or-minus 2 over 25 open parentheses 6 straight i with hat on top minus 8 straight j with hat on top minus 15 over 2 straight k with hat on top close parentheses close square brackets space straight m with rightwards arrow on top space equals plus-or-minus 4 open parentheses 6 straight i with hat on top minus 8 straight j with hat on top minus 15 over 2 straight k with hat on top close parentheses vector space space straight m with rightwards arrow on top space makes space obtuse space angle space with space straight Z minus axis. therefore space straight m with rightwards arrow on top. straight k with hat on top less than 0 therefore space straight m with rightwards arrow on top space equals plus 4 open parentheses 6 straight i with hat on top minus 8 straight j with hat on top minus 15 over 2 straight k with hat on top close parentheses space equals 24 straight i with hat on top minus 32 straight j with hat on top minus 30 straight k with hat on top end style
Answered by Vijaykumar Wani | 05 Dec, 2017, 04:27: PM

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