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If a^(2)+b^(2)+c^(2)=1 where, a,b,cin R,...

If `a^(2)+b^(2)+c^(2)=1` where, a,b,`cin R`, then the maximum value of `(4a-3b)^(2) + (5b-4c)^(2)+(3c-5a)^(2)` is

A

25

B

50

C

144

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let `r_(1)=ahati+bhatj+chatk, r_(2)=3hati+4hatj+5hatk`
`|vecr_(1) xx vecr_(2)| le|vecr_(1)|^(2) |vecr_(2)|^(2)`…………(1)
Now `vecr_(1) xx vecr_(2) = |{:(hati, hatj, hatk),(a,b,c),(3,4,5):}|`
`=hati(5b-4c)+hatj(3c-5a)+hatk(4a-b),`
So, from (1)
`(5b-4c)^(2)+(3c-5a)^(2)+(4a-3b)^(2)le50`
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