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If a=2hati+2hatj+3hatk, b=-hati+2hatj+hatk and c=3hati+hatj such that a + lambda b is perpendicular to c, then the value of lambda is |
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Answer» 2 ` andC=3hati+ hatj` Now` (a+ lamda b) BOT c` ` implies( a + LAMDAB).c =0` `[ :' `SCALAR PRODUCTOF twoperpendicularvectorsis zero] ` implies[( 2 hati + 2 hatj+ 3 hatk )+lamda (-hati + 2 hatj + hatk ) ].(3 hati+ hatj )=0 ` `implies [(2 - lamda) hati +(2+ 2 lamda ) hatj +(3+ lamda )hatk ] .(3 hati+ hatj) =0` ` implies(2- lamda )3+(2+2lamda )1+(3+lamda )0=0` `implies6-3lamda+ 2 +2 lamda =0` `implies8-lamda =0` `implies lamda =8` hence , therequied valueof ` lamda ` is 8 . |
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