यदि ` veca = 2 hati + 2 hatj + 3 hatk , vecb =- hati + 2 hatj + hatk` और ` vecc = 3 hati + hatj ` इस प्रकार है कि ` veca + lamda vecb , vecc` पर लम्ब है , तो `lamda ` का मान ज्ञात कीजिए ।

Explanation

दिए गए सदिश ` veca = 2 hati + 2hatj + 3 hatk , vecb =- hati + 2 hatj + hatk ` तथा ` vecc = 3 hati = 3 hati + hatj` है
अब ,` ( veca + lamda vecb bot vecc`( दिया है )
` implies ( veca + lamda vecb ) "." vecc= 0`
` implies [ ( 2 hati + 2 hatj + 3 hatk )+ lamda (- hati + 2hatj + 3hatk ) + 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 + 2 lamda ) 1+ (3 lamda )0=0`
`implies 6-3 lamda +2 +2 lamda =0`
`8-lamda =0 =8`
`implies lamda =8`