Let `veca=hati+4hatj+2hatk,vecb=3hati-2hatj+7hatk and vecc=2hati-2hatj+4hatk` . Find a vector `vecd` which perpendicular to both `veca and vecb and vecc.vecd=15`.

Explanation

Vector `vecd` is perpendicular to vectors `veca=hati+4hatj+2hatk,hatn=3hati-2hati-2hatj+7hatk`
`vecd=lambda|{:(hati,hatj,hatk),(1,4,2),(3,-2,7):}|=lambda(32hati-hatj-14hatk)`
`Also" " vecc.vecd=15`
`lambda(2hati-hatj+4hatk).(32hati-hatj-14hatk)15`
` or 9 lambda =15`
`or lambda = 5/3`
Hence, the required vector `vecd=1/3(160hati-5hatj-70hatk)`