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यदि सदिश `veca` और `vecb` के लिए `|veca+vecb|=sqrt(29)` और `vecaxx(2hati+3hatj+4hatk)=(2hati+3hatj+4hatk)xxvecb` है तब `(veca+vecb).(-7hati+2hatj+3hatk)` का एक सम्भावित मान ज्ञात कीजिए।

Answer» `vecaxx (2hati+3hatj+4hatk)=(2hati+3hatj+4hatk)xxvecb`
`:. vecaxx(2hati+3hatj+4hatk)=-vecbxx(2hati+3hatj+4hatk) [ vecaxxvecb=-vecbxxveca]`
`vecaxx(2hati+3hatj+4hatk)+vecb(2hati+3hatj+4hatk)=0`
`(2hati+3hatj+4hatkj)xx(veca+vecb)=0`
`veca+vecb=lamda(2hati=3hatj+4hatk)`
`sqrt(29)= +-lamdasqrt((2)^(2)+(3)^(2)+(4)^(2))`
`sqrt(29)=+-lamda(2+9+16)`
`sqrt(29)=+- lamda sqrt(29)`
`lamda=+-1 impliesveca+vecb(2hati+3hatj+4hatk)`
अब `(veca+vecb).(-7hati+2hatj+3hatk)=+-(2hati+3hatj+4hatk).(-7hati+3hatj+4hatk)`
`=+-(-14+6+12)`
`=+-4`


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