If →a=^i−^j,→b=−^j+2^k, then the value of (→a−2→b).(→a+→b) is
A
2
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B
-4
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C
6
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D
-9
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Solution
The correct option is D -9 →a−2→b=(^i−^j)−2(−^j+2^k) =(^i−^j)+2^j−4^k =(^i+^j−4^k)(→a+→b)=(^i−^j)+(−^j+2^k) =^i−^j−^j+2^k =(^i−2^j+2^k) Now ,(→a−2→b).(→a+→b) =(^i+^j−4^k).(^i−2^j+2^k) (1)(1)+(1)(−2)+(−4)(2)=−9 (→a−2→b).(→a+→b)=−9