1.

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

Answer»

2
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8

Solution :The givenvectorsare ` a = 2 hati+ 2 hatj + 3hatk, B=- hati+ 2hatj +hatk`
` 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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