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Let vec a= hat i+4 hat j+2 hat k , vec ...

Let ` vec a= hat i+4 hat j+2 hat k , vec b=3 hat i-2 hat j+7 hat ka n d vec c=2 hat i- hat j+4 hat kdot` Find a vector ` vec d` which is perpendicular to both ` vec a` and `vec b` and `vec c. vec d=15.`

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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)`
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