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]

Asked by mohdtayyab682 | 18 Jan, 2023, 10:34: PM

Expert Answer

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

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

-----------------------------------------

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

------------------------------------

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

Concept Videos