1.

Let a=hati+hatj+hatk, b=hati-hatj+hatkandc=hati-hatj-hatk be three vectors. A vector v in the plane of a and b, whose projection on c is (1)/(sqrt(3)), is given by

Answer»

`hati-3hatj+3hatk`
`-3hati-3hatj-hatk`
`3hati-hatj+3hatk`
`hati+3hatj-3hatk`

SOLUTION :Let`V=a+ lamda B`
`v=(1+lamda )hati +(1-lamda ) hatj +(1+lamda )hatk`
projectionofvonc`=(v.c)/(|c|)=(1)/(sqrt(3))`
`IMPLIES ((1+lamda )-(1-lamda )-(1+lamda ))/(sqrt(3))=(1)/(sqrt(3))`
`implies lamda =2`
`thereforev= 3 hati- hatj+ 3 hatk`


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