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CBSE Class 12-science Answered

If |𝑎⃗| = 3 and −1 ≤ 𝑘 ≤ 2, then |𝑘𝑎⃗| lies in the interval (a) [0,6] (b) [−3,6] (c) [3,6] (d) [1,2]
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Asked by mohdtayyab682 | 18 Jan, 2023, 10:34: PM
answered-by-expert Expert Answer
If  begin mathsize 14px style open vertical bar a with rightwards arrow space on top close vertical bar space space equals space 3 end style , then begin mathsize 14px style a with rightwards arrow on top space equals space minus 3 space u with hat on top end style  or   begin mathsize 14px style a with rightwards arrow on top space equals space 3 space u with hat on top end style
 
Let begin mathsize 14px style a with rightwards arrow on top space equals space minus 3 space u with hat on top end style
if k = -1   , then begin mathsize 14px style open vertical bar k space a with rightwards arrow on top close vertical bar space equals space 3 end style ;
if k = 0   , then begin mathsize 14px style open vertical bar k space a with rightwards arrow on top close vertical bar space equals space 0 end style ;
if k = 1   , then begin mathsize 14px style open vertical bar k space a with rightwards arrow on top close vertical bar space equals space 3 end style ;
if k = 2   , then begin mathsize 14px style open vertical bar k space a with rightwards arrow on top close vertical bar space equals space 6 end style
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Let begin mathsize 14px style a with rightwards arrow on top space equals space 3 space u with hat on top end style
if k = -1   , then begin mathsize 14px style open vertical bar k space a with rightwards arrow on top close vertical bar space equals space 3 end style ;
if k = 0   , then begin mathsize 14px style open vertical bar k space a with rightwards arrow on top close vertical bar space equals space 0 end style ;
if k = 1   , then begin mathsize 14px style open vertical bar k space a with rightwards arrow on top close vertical bar space equals space 3 end style ;
if k = 2   , then begin mathsize 14px style open vertical bar k space a with rightwards arrow on top close vertical bar space equals space 6 end style
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Hence begin mathsize 14px style open vertical bar k space a with rightwards arrow on top close vertical bar end style lies in the interval ( 0, 6 )
 
Answered by Thiyagarajan K | 19 Jan, 2023, 07:59: AM
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