1.

A vector coplanar with vectoreshati+ hatjandhatj + hatkand parallel to the vector2 hati- 2 hatj- 4hatk is

Answer»

`HATI - hatk`
`hati - hatj -2HATK `
`hati +hatj-hatk `
`3hati+3hatj-6hatk`

Solution :Any vector COPLANAR with vectors ` hati+ hatj andhatj +hatk ` is
`a=x (hati +hatj)+y (hatj +hatk)`
`impliesa=xhati +(x+y)hatj +yhatk`
Itis giventhata isparaallelto` 2 hati- 2 hatj- 4 hatk `
` thereforea= LAMDA( 2 hati- 2hatj- 4 hatk )` for some SCALAR ` lamda `.
`implies [ x hati +(x+y)hatj +yhatk ]= lamda (2 hati- 2hatj - 4 hatk)`
`implies x= 2 lamda , x+y=- 2 lamdaandy=- 4 lamda `
`implies x=2lamdaandy=-4 lamda `
`thereforea= 2 lamda( hati - hatj- 2hatk )` , where`lamda inR.`


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